• TABLE OF CONTENTS
HIDE
 Front Cover
 Title Page
 Acknowledgement
 Table of Contents
 List of Figures
 List of Tables
 List of symbols
 Abstract
 Introduction
 Background information
 Mud fluidization by waves
 Sediment transport modeling
 Sorption kinetics
 Constituent transport modeling
 Flume experiments
 Results, discussion and conclu...
 Appendix A: Flume experimental...
 Appendix B: Simulated and measured...
 Bibliography
 Biographical sketch






Group Title: Technical report – University of Florida. Coastal and Oceanographic Engineering Program ; 111
Title: Sediment-associated constituent release at the mud-water interface due to monochromatic waves
CITATION PAGE IMAGE ZOOMABLE
Full Citation
STANDARD VIEW MARC VIEW
Permanent Link: http://ufdc.ufl.edu/UF00075491/00001
 Material Information
Title: Sediment-associated constituent release at the mud-water interface due to monochromatic waves
Series Title: UFLCOEL-TR
Physical Description: xxxi, 313 p. : ill. ; 28 cm.
Language: English
Creator: Li, Yigong, 1964-
University of Florida -- Coastal and Oceanographic Engineering Dept
Publisher: Coastal & Oceanographic Engineering Dept., University of Florida
Place of Publication: Gainesville Fla
Publication Date: 1996
 Subjects
Subject: Suspended sediments -- Mathematical models   ( lcsh )
Sediment transport -- Mathematical models   ( lcsh )
Mud -- Mathematical models   ( lcsh )
Contaminated sediments -- Mathematical models   ( lcsh )
Coastal and Oceanographic Engineering thesis, Ph. D
Dissertations, Academic -- Coastal and Oceanographic Engineering -- UF
Genre: government publication (state, provincial, terriorial, dependent)   ( marcgt )
bibliography   ( marcgt )
non-fiction   ( marcgt )
 Notes
Thesis: Thesis (Ph. D.)--University of Florida, 1996.
Bibliography: Includes bibliographical references (p. 296-312).
Statement of Responsibility: by Yigong Li.
Funding: This publication is being made available as part of the report series written by the faculty, staff, and students of the Coastal and Oceanographic Program of the Department of Civil and Coastal Engineering.
 Record Information
Bibliographic ID: UF00075491
Volume ID: VID00001
Source Institution: University of Florida
Holding Location: University of Florida
Rights Management: All rights reserved, Board of Trustees of the University of Florida
Resource Identifier: oclc - 35915799

Table of Contents
    Front Cover
        Front Cover
    Title Page
        Title Page
    Acknowledgement
        Acknowledgement 1
        Acknowledgement 2
    Table of Contents
        Table of Contents 1
        Table of Contents 2
        Table of Contents 3
        Table of Contents 4
    List of Figures
        List of Figures 1
        List of Figures 2
        List of Figures 3
        List of Figures 4
        List of Figures 5
    List of Tables
        List of Tables 1
        List of Tables 2
    List of symbols
        Unnumbered ( 16 )
        Unnumbered ( 17 )
        Unnumbered ( 18 )
        Unnumbered ( 19 )
        Unnumbered ( 20 )
        Unnumbered ( 21 )
        Unnumbered ( 22 )
        Unnumbered ( 23 )
        Unnumbered ( 24 )
        Unnumbered ( 25 )
        Unnumbered ( 26 )
        Unnumbered ( 27 )
        Unnumbered ( 28 )
        Unnumbered ( 29 )
        Unnumbered ( 30 )
    Abstract
        Abstract 1
        Abstract 2
    Introduction
        Page 1
        Page 2
        Page 3
        Page 4
        Page 5
        Page 6
        Page 7
        Page 8
    Background information
        Page 9
        Page 10
        Page 11
        Page 12
        Page 13
        Page 14
        Page 15
        Page 16
        Page 17
        Page 18
        Page 19
        Page 20
        Page 21
        Page 22
        Page 23
        Page 24
        Page 25
        Page 26
        Page 27
        Page 28
        Page 29
        Page 30
        Page 31
        Page 32
        Page 33
        Page 34
        Page 35
        Page 36
        Page 37
        Page 38
        Page 39
        Page 40
        Page 41
        Page 42
        Page 43
        Page 44
        Page 45
        Page 46
        Page 47
        Page 48
        Page 49
        Page 50
        Page 51
        Page 52
        Page 53
        Page 54
        Page 55
        Page 56
        Page 57
        Page 58
        Page 59
        Page 60
        Page 61
        Page 62
        Page 63
    Mud fluidization by waves
        Page 64
        Page 65
        Page 66
        Page 67
        Page 68
        Page 69
        Page 70
        Page 71
        Page 72
        Page 73
        Page 74
        Page 75
        Page 76
        Page 77
        Page 78
        Page 79
        Page 80
        Page 81
        Page 82
        Page 83
        Page 84
        Page 85
        Page 86
        Page 87
        Page 88
        Page 89
        Page 90
        Page 91
        Page 92
        Page 93
        Page 94
        Page 95
        Page 96
        Page 97
        Page 98
        Page 99
        Page 100
        Page 101
    Sediment transport modeling
        Page 102
        Page 103
        Page 104
        Page 105
        Page 106
        Page 107
        Page 108
        Page 109
        Page 110
        Page 111
        Page 112
        Page 113
        Page 114
        Page 115
        Page 116
        Page 117
        Page 118
        Page 119
        Page 120
        Page 121
        Page 122
        Page 123
        Page 124
        Page 125
        Page 126
        Page 127
        Page 128
        Page 129
        Page 130
        Page 131
        Page 132
        Page 133
        Page 134
        Page 135
        Page 136
        Page 137
        Page 138
        Page 139
        Page 140
        Page 141
        Page 142
        Page 143
        Page 144
        Page 145
        Page 146
        Page 147
        Page 148
        Page 149
        Page 150
        Page 151
    Sorption kinetics
        Page 152
        Page 153
        Page 154
        Page 155
        Page 156
        Page 157
        Page 158
        Page 159
        Page 160
        Page 161
        Page 162
        Page 163
        Page 164
        Page 165
        Page 166
        Page 167
        Page 168
        Page 169
        Page 170
        Page 171
        Page 172
        Page 173
    Constituent transport modeling
        Page 174
        Page 175
        Page 176
        Page 177
        Page 178
        Page 179
        Page 180
        Page 181
        Page 182
        Page 183
        Page 184
        Page 185
        Page 186
        Page 187
        Page 188
        Page 189
        Page 190
        Page 191
        Page 192
        Page 193
        Page 194
        Page 195
        Page 196
        Page 197
    Flume experiments
        Page 198
        Page 199
        Page 200
        Page 201
        Page 202
        Page 203
        Page 204
        Page 205
        Page 206
        Page 207
        Page 208
        Page 209
        Page 210
        Page 211
        Page 212
        Page 213
        Page 214
        Page 215
        Page 216
        Page 217
        Page 218
        Page 219
        Page 220
        Page 221
        Page 222
        Page 223
        Page 224
    Results, discussion and conclusions
        Page 225
        Page 226
        Page 227
        Page 228
        Page 229
        Page 230
        Page 231
        Page 232
        Page 233
        Page 234
        Page 235
        Page 236
        Page 237
        Page 238
        Page 239
        Page 240
        Page 241
        Page 242
        Page 243
        Page 244
        Page 245
        Page 246
        Page 247
        Page 248
        Page 249
        Page 250
        Page 251
        Page 252
        Page 253
        Page 254
        Page 255
        Page 256
    Appendix A: Flume experimental data
        Page 257
        Page 258
        Page 259
        Page 260
        Page 261
        Page 262
        Page 263
        Page 264
        Page 265
        Page 266
        Page 267
        Page 268
    Appendix B: Simulated and measured suspended sediment and dye concentration profiles
        Page 269
        Page 270
        Page 271
        Page 272
        Page 273
        Page 274
        Page 275
        Page 276
        Page 277
        Page 278
        Page 279
        Page 280
        Page 281
        Page 282
        Page 283
        Page 284
        Page 285
        Page 286
        Page 287
        Page 288
        Page 289
        Page 290
        Page 291
        Page 292
        Page 293
        Page 294
        Page 295
    Bibliography
        Page 296
        Page 297
        Page 298
        Page 299
        Page 300
        Page 301
        Page 302
        Page 303
        Page 304
        Page 305
        Page 306
        Page 307
        Page 308
        Page 309
        Page 310
        Page 311
        Page 312
    Biographical sketch
        Page 313
Full Text



UFL/COEL-TR/111


SEDIMENT-ASSOCIATED CONSTITUENT RELEASE
AT THE MUD-WATER INTERFACE DUE TO
MONOCHROMATIC WAVES






by



Yigong Li


Dissertation


1996















SEDIMENT-ASSOCIATED CONSTITUENT RELEASE AT
THE MUD-WATER INTERFACE DUE TO MONOCHROMATIC WAVES












By

YIGONG LI


A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL
OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT
OF THE REQUIREMENTS FOR THE DEGREE OF
DOCTOR OF PHILOSOPHY

UNIVERSITY OF FLORIDA


1996













ACKNOWLEDGMENT


First of all, I would like to express my deepest gratitude to my advisor and the

chairman of my supervisory committee Professor Ashish J. Mehta, for his constructive

direction, enthusiasm, advice and unflagging support throughout this four year study, which

has been a challenging, joyful and unforgettable experience in my life.

I wish to thank Professors Kirk Hatfield and Robert G. Dean for their continuously

valuable advice, suggestions and discussions. Thanks are also due to the other committee

members, including Professor Peter Y. Sheng and Professor Brij M. Moudgil for their advice,

comments and patience in reviewing this dissertation.

Appreciation is extended to all other faculty members in the department, as well as

those in the Department of Aerospace Engineering Mechanics and Engineering Science,

Civil Engineering, Agricultural Engineering, Soil Science and Chemical Engineering for

supplying various components of knowledge essential for the pursuit of this study through

their creative teaching efforts.

Gratitude is due to departmental staff, especially, Mr. Sydney Schofield, Mr. Jim

Joiner and Mr. George Chappell at the Coastal Engineering Laboratory for their cooperation

and help during the experimental phase of this research. Support also came from many

friends and fellow research assistants.








Special thanks go to Sandra Bivins, Becky Hudson, Lucy Hamm, Cynthia Vey, John

Davis and Helen Twedell for their kindness, which helped directly or indirectly in the

completion of this study. Deep appreciation goes to Dr. Feng Jiang, Dr. Xinjian Chen and

Dr. Say-Chong Lee, with whose help I got through the hard initial period of my stay in

Gainesville. Appreciation also goes to Mr. Paul Devine, Mr. Ahmad Tarigan, Mr. Hogo

Rodriguez, Ms. Xu Wang, Ms. Jie Zheng, Dr. Taerim Kim, Mr. Eduardo Yassuda, Mr. Mike

Krecic and Mr. Albert Browder for their assistance and useful discussions.

Funding for this work came from U.S. Army Engineer Waterways Experiment

Station at Vicksburg, Mississippi. The contaminant portion of the work was funded by

contract DACW39-95-K-0023 through the Environmental Laboratory, and the sediment part

by contract DACW39-95-K-0022 through the Hydraulics Laboratory. Assistance provided

especially by Dr. Mark Dortch and Dr. T.M. Parchure in processing the contracts, managing

them and providing valuable technical guidance is sincerely acknowledged.

My final acknowledgement is reserved for those whom I probably owe the most, my

wife, Wendy S. Tan, for her love, support, encouragement and patience throughout these

four years, and my parents, who instilled in me the work ethic and values that have allowed

me to make it this far, and have supported me all my life.














TABLE OF CONTENTS



ACKNOWLEDGMENT ................................... ......... ii

LIST OFFIGURES .................................................... viii

LIST OFTABLES .................................................... xiii

LIST OF SYMBOLS ................................................... xv

ABSTRACT ........................................................ xxx

1 INTRODUCTION ................................................... 1
1.1 Problem Statement ........................................... 1
1.2 Objective, Tasks and Scope ....................................... 5
1.3 Outline of Presentation ........................................ 7

2 BACKGROUND INFORMATION ...................................... 9
2.1 Introduction ............ .......................................9
2.2 Mud Rheology and Wave-Mud Interaction Modeling ................. 9
2.2.1 Mud Rheology .........................................10
2.2.2 Wave-Mud Interaction Modeling .................................. 19
2.3 Mud Fluidization and Fluid Mud .................................23
2.4 Processes Governing the Vertical Structure of Suspension ............. 28
2.4.1 Settling ................ ........................... 28
2.4.2 Diffusion ..... .................... .................... 31
2.4.3 Deposition Rate .................................... .35
2.4.4 Entrainment .......................................... 36
2.5 Sorption Models ............................................... 40
2.5.1 Equilibrium Sorption Isotherm ........................... 40
2.5.2 Kinetic Sorption Models ................................ 43
2.5.3 Advanced Sorption Models ............................. 46
2.6 Sediment-Associated Contaminant Transport ........................ 49
2.6.1 Contaminant Transport in Water .......................... 49
2.6.2 Contaminant Transport in Bottom Sediment ................. 52
2.6.3 Fluxes Across the Sediment-Water Interface ................ 58








2.6.4 Fluxes Across the Fluid Mud-Bed Interface .................. 62

3 MUD FLUIDIZATION BY WAVES ................................... 64
3.1 Introduction ................................................. 64
3.2 Mechanics of Fluidization ................ .................... 65
3.2.1 Vertical and Horizontal Motions of Bed under Waves ......... 65
3.2.2 Bed Failure by Horizontal Forces ......................... 66
3.2.3 Bed Fluidization by Vertical Forces ....................... 68
3.2.4 A Heuristic Criterion for Bed Fluidization Under Waves ....... 70
3.3 Voigt and Extensional-Voigt Models .............................72
3.4 Bed as a Spring-Dashpot-Mass System ............................ 74
3.4.1 Case 1: G,, and pn Independent of Depth .................... 75
3.4.2 Case 2: G,, and pn Increase with Depth ..................... 77
3.5 Dynamic Response of Bed .....................................79
3.5.1 Wave over Bed: One-Degree of Freedom ................... 79
3.5.2 Wave over Fluid Mud above Bed: Two-Degrees of Freedom .... 80
3.6 Fluidization Depth ............................................ 83
3.6.1 M odel Results ........................................ 83
3.6.2 Comparison with Data ................................ 90
3.7 Application to Field Data ..................................... 93
3.7.1 Field Conditions ......................................93
3.7.2 Model Application .................................... 96
3.8 Conclusions ................................................. 99

4 SEDIMENT TRANSPORT MODELING ............................... 102
4.1 Introduction ................................................ 102
4.2 Three-Layered System ........................................ 102
4.3 Wave-Averaged Transport Equation for Constituent Transport ......... 103
4.4 Sediment Transport Model ................................... 107
4.4.1 Vertical Fine-grained Sediment Transport Equation .......... 107
4.4.2 Boundary Conditions .................................. 110
4.5 Fluid Mud Entrainment Rate ................................... 112
4.5.1 Entrainment Rate Formulation ........................... 112
4.5.2 Laboratory Experiment ............................... 115
4.5.3 Critical Global Richardson Number for Entrainment ......... 118
4.5.4 Comparison with Experimental Data ...................... 124
4.6 Laboratory Simulations ...................................... 128
4.7 Model Application to Field Data .............................. 132
4.7.1 Coast of Louisiana ................ .................. 133
4.7.2 Southwest Coast of India ............................... 142

5 SORPTION KINETICS .............................................. 152
5.1 Introduction ............................................152









5.2 Dyes, Sediments and Fluid Characteristics ......................... 153
5.3 Sorption Test Procedure ..................................... 155
5.3.1 Sampling of Sediment-Dye-Water Mixture ................. 155
5.3.2 Photographic Method for Dye Concentration Determination
in Water ................ ......................... 156
5.3.3 Calibration Experiments ............................... 158
5.4 Results and Discussion ................ ...................... 160
5.4.1 Sorption Isotherms ................................... 160
5.4.2 Sorption Kinetics ..................................... 164
5.4.3 Discussion .......................................... 169

6 CONSTITUENT TRANSPORT MODELING ........................... 174
6.1 Introduction ................................................ 174
6.2 Constituent Transport Model .................................. 174
6.2.1 Formulation ......................................... 174
6.2.2 Governing Equations .................................. 176
6.2.3 Boundary and Interfacial Connective Conditions ............ 178
6.3 Wave-Induced Diffusivity in Fluid Mud, Ka ........................ 184
6.4 Mass Transfer Coefficient, K,2 ................................ 190
6.5 Solution Technique .......................................... 196

7 FLUME EXPERIMENTS ........................................... 198
7.1 Introduction ................................................ 198
7.2 Experimental Equipment ......................................198
7.2.1 Wave Flume ......................................... 198
7.2.2 Colorimeter ......................................... 199
7.3 Test Conditions and Procedure .................................. 204
7.3.1 Test Conditions ................ .................... 204
7.3.2 Procedure ................ ......................... 204
7.4 Data Analysis ............................................ 206
7.4.1 Suspended Sediment ................................. 206
7.4.2 Dye Release in Water ................................... 215

8 RESULTS, DISCUSSION AND CONCLUSIONS ......................... 225
8.1 Introduction ................................................225
8.2 Results of Model Simulations and Calibrations ..................... 225
8.2.1 Model Conditions ............ ........................225
8.2.2 Suspended Sediment Concentrations ...................... 230
8.2.3 Dye Concentrations ................ .................. 233
8.3 Analysis and Discussion ..................................... 238
8.3.1 Release Flux and Sub-fluxes ........................... 238
8.3.2 Effects on Release Sub-fluxes ........................... 243
8.4 Summary and Conclusions ...................................... 250









8.5 Recommendations for Future Studies ............................. 254

APPENDICES

A FLUME EXPERIMENTAL DATA ....................................257

B SIMULATED AND MEASURED SUSPENDED SEDIMENT
AND DYE CONCENTRATION PROFILES ........................ 269
B.1 Suspended Sediment Profiles .................................. 269
B.2 Dye Concentration Profiles in Water ............................. 280

BIBLIOGRAPHY .................................................... 296

BIOGRAPHICAL SKETCH ........................................... 313













LIST OF FIGURES


1.1 Total contaminant flux and sub-fluxes. .................................. 2
2.1 Common two-parameter viscoelastic models. ............................. 13
2.2 Jeffrey models. ..................................................... 14
2.3 A typical wave-mud system (after Hwang, 1989) ........................... 23
2.4 Schematic of instantaneous stress profile in a wave-mud system
(after Mehta et al., 1994). ......................................... 24
2.5 Three-layered water-fluid mud-bed system and
vertical sediment transport processes under waves........................ 25
2.6 A schematic description of settling velocity and flux variation
with suspension concentration (after Hwang, 1989)....................... 29
2.7 Sediment-associated contaminant transport processes. ....................... 49
3.1 Forces on a particle or floc........................................... 68
3.2 Bed simulated as a S-D-M system with known vertical distributions of bed density,
p, extensional elastic modulus, Gn, and extensional viscous coefficient, i,. ... 74
3.3 Bed layer represented by a one-degree of freedom system. ................... 80
3.4 Fluid mud and bed layers represented by a two-degrees of freedom system ....... 81
3.5 A schematic description of the criterion for equilibrium fluidization depth, z'c. ... 83
3.6 Fluidization depth variation with wave frequency and amplitude
with negligible cohesion and without considering initial fluid mud effects .... 84
3.7 Fluidization depth variation with wave frequency and bed elastic modulus
with negligible cohesion and without considering initial fluid mud effects. ... 85
3.8 Fluidization depth variation with wave frequency and bed viscous coefficient
with negligible cohesion and without considering initial fluid mud effects. .... 85
3.9 Fluidization depth variation with wave frequency and amplitude
with negligible cohesion, but including initial fluid mud effects. ............. 87
3.10 Fluidization depth variation with wave frequency and bed elastic modulus
with negligible cohesion, but including initial fluid mud effects. ............ 87
3.11 Fluidization depth variation with wave frequency and bed viscous coefficient
with negligible cohesion, but including initial fluid mud effects. ............. 88
3.12 Fluidization depth variation with wave frequency and cohesion parameter. ..... 89
3.13 Comparison.between calculated and flume-measured fluidization depths. ...... 92
3.14 Bathymetric map of Lake Okeechobee. Depth are relative to a datum
which is 3.81 m above msl (after Mehta and Jiang, 1990) ................. 94
3.15 Mud thickness contour map of Lake Okeechobee (after Kirby et al., 1989). ..... 95
3.16 A representative bottom mud density profile in Lake Okeechobee. ............ 97








3.17 Calculated fluidization depth as a function of water depth in Lake Okeechobee
and band of measured values. ..................................... 98
3.18 An example of fluidization depth calculation for Lake Okeechobee at a site
where water depth was 1.43 m. ..................................... 98
4.1 Three-layered system and vertical sediment transport processes considered. .... 102
4.2 Side view of wave flume used in entrainment experiments................... 115
4.3 Critical Richardson Number for entrainment by waves ...................... 121
4.4 Critical Richardson Number estimated from the experiments of Maa (1986) .... 121
4.5 Dimensionless entrainment rate as a function of Richardson Number. ......... 125
4.6 Entrainment flux as a function of wave height and mud viscosity. ............. 127
4.7 Comparison between simulated and measured data for Run 4 of Maa (1986). ... 130
4.8 Comparison between simulated and measured data for Run 5 of Maa (1986). ... 130
4.9 Comparison between simulated and measured data for Run 6 of Maa (1986). ... 131
4.10 Location map of the study area of Kemp (1986). ........................ 135
4.11 Simulated and measured data (Kemp, 1986) for the Louisiana coast
during frontal passage. ............................................ 139
4.12 Simulated and measured data (Kemp, 1986) for the Louisiana coast
during the post-frontal period. ..................................... 140
4.13 Location map of the study area of Mathew (1992) off Alleppey
in the State of Kerala, India. ..................................... 143
4.14 A conceptual model of mudbank evolution ............................. 143
4.15 Settling velocity data used for mudbank turbidity simulation ............... 150
4.16 Simulated suspended sediment concentration profiles and data of Mathew (1992)
in the vicinity of Alleppey Pier...................................... 151
5.1 Schematic diagram of the sorption procedure. ............................. 156
5.2 Schematic diagram for photography in sorption tests. ...................... 157
5.3 Procedure for determining dye concentration ............................. 157
5.4 Calibration curve for Rhodamine B solutions. ............................ 159
5.5 Calibration curve for Erioglaucine A solutions ............................ 160
5.6 Linear isotherm of Rhodamine B sorbed onto kaolinite. ..................... 161
5.7 Linear isotherm of Rhodamine B sorbed onto AK mud. ..................... 161
5.8 Linear isotherm of Erioglaucine A sorbed onto kaolinite. ................... 162
5.9 Linear isotherm of Erioglaucine A sorbed onto AK mud. ................... 163
5.10 Effect of temperature on sorption of Rhodamine B on kaolinite ............. 163
5.11 Comparison between kinetic sorption model and experimental data. ......... 167
5.12 Comparison between kinetic sorption model and experimental .............. 167
5.13 Comparison between kinetic sorption model and experimental data. ......... 168
5.14 Comparison between kinetic model and experimental results................ 168
5.15 Comparison between kinetic sorption model and experimental data. ......... 169
5.16 Chemical structures of Rhodamine B and Erioglaucine A .................. 169
5.17 Idealized clay geometries of kaolinite and attapulgite. ...................... 170
6.1 Sediment-associated contaminant transport processes considered. ............. 175
6.2 Contaminant fluxes across the water-fluid mud and fluid mud-bed interfaces. ... 179








6.3 Schematic representation of the mode of indirect dissolved and
particulate contaminant transport across the water-mud interface ........... 183
6.4 Schematic of energy transport and dissipation, velocity distribution and
momentum transport, and constituent concentration distribution and
momentum-analogous constituent mass transport ...................... 188
6.5 Schematic shown of bottom diffusive sub-layer and wave boundary layer in water,
and direct convective flux........................ .......... ......... 191
7.1 Wave flume used in experiments ........................ .............. 199
7.2 Relationship between incident wave length and transmittance for Rhodamine B.. 201
7.3 Relationship between incident wave length and transmittance for Erioglaucine A. 201
7.4 Calibration of Rhodamine B concentration with selected light wave length,
LRB= 550nm.................................................. 202
7.5 Calibration of Erioglaucine A concentration with selected light wave length,
LEA = 625 nm.................................................... 202
7.6 Suspended sediment concentration profile variations with time at B, C and D
in the duration range of 240 ~ 480 minutes ............................ 207
7.7 Suspended sediment concentration profile variations with time at A and E
in the duration range of 240 480 minutes. ......................... 208
7.8 Suspended sediment concentration profile variations with time at B, C and D
in the duration range of 480 ~ 720 minutes. ........................... 209
7.9 Suspended sediment concentration profile variations with time at A and E
in the duration range of 480 ~ 720 minutes. ........................... 210
7.10 Comparison between the calculated suspended sediment concentration
using three methods (Eqs. 7.7,7.10 and 7.11). ......................... 214
7.11 Dye concentration profile variations with time at B, C and D
in the duration range of 0 240 minutes. .......................... .215
7.12 Dye concentration profile variations with time at A and E
in the duration range of 0 ~ 240 minutes. ............................. 217
7.13 Dye concentration profile variations with time at B, C and D
in the duration range of 240 480 minutes ............................ 218
7.14 Dye concentration profile variation with time at A and E
in the duration range of 240 480 minutes ............................ 219
7.15 Dye concentration profile variations with time at B, C and D
in the duration range of 480 720 minutes. ........................... 220
7.16 Dye concentration profile variations with time at B, C and D
in the duration range of 480 720 minutes. .......................... 221
7.17 Comparison between calculated dye concentration using three methods
(Eqs. 7.12, 7.15 and 7.16).............................. ........... 223
8.1 Comparison between simulated and measured depth-averaged
suspended sediment concentrations in Test 2 ........................... 230
8.2 Comparison between simulated and measured depth-averaged
suspended sediment concentrations in Test 3 ........................... 231








8.3 Comparison between simulated and measured depth-averaged
suspended sediment concentrations in Test 4 ............
8.4 Comparison between simulated and measured depth-averaged
suspended sediment concentrations in Test 5 ............
8.5 Comparison between simulated and measured depth-averaged
suspended sediment concentrations in Test 6 ............
8.6 Comparison between simulated and measured depth-averaged
dye concentrations in Test 1. .....................
8.7 Comparison between simulated and measured depth-averaged
dye concentrations in Test2. ..........................
8.8 Comparison between simulated and measured depth-averaged
dye concentrations in Test 3. .......................
8.9 Comparison between simulated and measured depth-averaged
dye concentrations in Test4. .......................
8.10 Comparison between simulated and measured depth-averaged
dye concentrations in Test 5 ......................
8.11 Comparison between simulated and measured depth-averaged
dye concentrations in Test 6. ..... ..... ...........
8.12 Dye release flux and sub-fluxes in Tests 1-1 (0-240 min)
and 1-2(240-480 min) ..............................


.............. 231

.............. 232

.............. 232

..............235

..............235

..............236

..............236

..............237

..............237

..............238


8.13 Dye release flux and sub-fluxes in Tests 2-1(0-240 min), 2-2 (240-480 min)
and 2-3 (480-600 min). ..........................................239
8.14 Dye release flux and sub-fluxes in Tests 3-1 (0-240 min)
and 3-2(240-480 min). ..........................................239
8.15 Dye release flux and sub-fluxes in Test 4 (0-720 min). ..................... 240
8.16 Dye release flux and sub-fluxes in Tests 5-1(0-240 min), 5-2 (240-480 min)
and 5-3 (480-600 min) ........................................ 240
8.17 Dye release flux and sub-fluxes in Tests 6-1(0-240 min), 6-2 (240-480 min)
and 6-3 (480-600 min) ...........................................241
8.18 Schematic shown characteristic profiles and coefficients
related to release fluxes............................................ 244
8.19 Relationship between the direct convective flux coefficient, 12c,
and the bottom boundary layer Richardson Number, Ri ................... 246
8.20 Relationship between dimensionless diffusivity in fluid mud, D/v,,
and the dimensionless wave damping parameter, H2ki/(h2-h,) .............. 248
B. 1 Comparison between simulated and measured suspended sediment profiles
in Test 2-2. .................................................... 269
B.2 Comparison between simulated and measured suspended sediment profiles
in Test 2-3..................................................... 270
B.3 Comparison between simulated and measured suspended sediment profiles
in Test 3-2. .................................................... 271
B.4 Comparison between simulated and measured suspended sediment profiles
In Test 3-3. .................................................... 272








B.5 Comparison between simulated and measured suspended sediment profiles
in Test 4-1 during time range of 0 300 min. .......................... 273
B.6 Comparison between simulated and measured suspended sediment profiles
in Test 4-1 during time range of 300 660 min. ........................ 274
B.7 Comparison between simulated and measured suspended sediment profiles
in Test 5-2 during time range of 240 480 min ........................ 275
B.8 Comparison between simulated and measured suspended sediment profiles
in Test 5-3 during time range of 480 720 min ........................ 276
B.9 Comparison between simulated and measured suspended sediment profiles
in Test 6-1 during time range of 0 240 min .......................... 277
B.10 Comparison between simulated and measured suspended sediment profiles
in Test 6-2 during time range of 240 480 min. ........................ 278
B. 11 Comparison between simulated and measured suspended sediment profiles
in Test 6-3 during time range of 480 ~ 720 min. ........................ 279
B.12 Comparison between simulated and measured dye profiles in Tests 1-1. ...... 280
B.13 Comparison between simulated and measured dye profiles in Tests 1-2. ...... 281
B.14 Comparison between simulated and measured dye profiles in Tests 2-1 ....... 282
B.15 Comparison between simulated and measured dye profiles in Test 2-2. ....... 283
B.16 Comparison between simulated and measured dye profiles in Test 2-3. ...... 284
B.17 Comparison between simulated and measured dye profiles in Test 3-1. ....... 285
B.18 Comparison between simulated and measured dye profiles in Test 3-2. ...... 286
B.19 Comparison between simulated and measured dye profiles in Test 3-3 ....... 287
B.20 Comparison between simulated and measured dye profiles in Test 4
during time range of 0 300 min. .................................. 288
B.21 Comparison between simulated and measured dye profiles in Test 4
during time range of 300 660 min. .................................289
B.22 Comparison between simulated and measured dye profiles in Test 5-1
during time range of 0 240 min ......................................290
B.23 Comparison between simulated and measured dye profiles in Test 5-2
during time range of 240 480 min. ................................ 291
B.24 Comparison between simulated and measured dye profiles in Test 5-3
during time range of 480 720 min ................................ 292
B.25 Comparison between simulated and measured dye profiles in Test 6-1
during time range of 0 ~ 240 min ...................................293
B.26 Comparison between simulated and measured dye profiles in Test 6-2
during time range of 240 480 min. ................................. 294
B.27 Comparison between simulated and measured dye profiles in Test 6-3
during time range of 480 720 min ................................. 295














LIST OF TABLES


2.1 Diffusion coefficients for some tracers in some typical marine mud beds. ....... 57
3.1 Wave and bed conditions and calculated and measured fluidization depths. ...... 91
3.2 Summary of selected fluid mud generation experiments in flumes from Ross(1988)
and Lindenberg et al. (1989) ........................................91
3.3 Flume tests of Lindenberg et al. (1989) without fluid mud generation .......... 93
4.1 Experimental results for determination of the critical entrainment condition. .... 117
4.2 Equilibrium depth-averaged suspended sediment concentrations
for specified wave conditions. ..................................... 119
4.3 Parameters for simulating Runs 4, 5 and 6 of Maa (1986). .................. 134
4.4 Measured wave and suspended sediment data from Louisiana coast
(based on Kemp, 1986). .......................................... 136
4.5 Parameters for simulating data from the Louisiana coast. ................... 138
4.6 Parameters for simulating field data of Mathew (1992)
from the southwest coast of India. .................................. 147
5.1 Physical and chemical properties of Rhodamine B and Erioglaucine A. ........ 153
5.2 Chemical compositions of kaolinite and attapulgite (%) .................... 154
5.3 Chemical composition of tap water. ................................... 155
5.4 Equilibrium sorption distribution coefficient, Kd (1/g) ...................... 161
5.5 First order rate coefficient for sorption kinetics ............. ............ 172


7.1 Tests Conditions ..................................
8.1 Characteristic parameters for modeling of Tests 1 and 2....
8.2 Characteristic parameters for modeling of Tests 3 and 4....
8.3 Characteristic parameters for modeling for Tests 5 and 6...
A. 1 Sediment concentration (g/1) data for Test 1 ............
A.2 Sediment concentration (g/1) data for Test 2 ............
A.3 Sediment concentration (g/1) data for Test 3 ............
A.4 Sediment concentration (g/1) data for Test 4 ............
A.5 Sediment concentration (g/1) data for Test 5 ............
A.6 Sediment concentration (g/l) data for Test 6 ............
A.7 Dye concentration (mg/1) data for Test 1 ...............
A.8 Dye concentration (mg/1) data for Test 2 ...............
A.9 Dye concentration (mg/1) data for Test 3 ...............
A. 10 Dye concentration (mg/1) data for Test 4 ..............
A. 11 Dye concentration (mg/1) data for Test 5 ..............
A. 12 Dye concentration (mg/1) data for Test 6 ..............


........... 203
............. 227
............. 228
............. 229
............. 257
............. 257
............. 258
............. 259
............. 259
............. 260
.......... 261
............. 262
............. 263
............. 265
............. 266
............. 267








A. 13 Temperature measurements (oC) ..................................... 268













LIST OF SYMBOLS


Ae = Empirical coefficient

ab = Amplitude of near-bed wave-induced horizontal excursion

B = Coefficient in relationship between constituent concentration and light intensity

B', B" = Characteristic coefficients in relationship between constituent concentration and

light intensity

C, Cd = Constituent concentration in water

Cb = Constituent concentration just outside the bottom diffusive layer in water

Ceq = Constituent concentration in water at equilibrium

Cdo = Initial constituent concentration in water

Cid = Constituent concentration in water layer

C2d = Constituent concentration in pore water in fluid mud

C3d = Constituent concentration in pore water in bed

Cd. = Final or equilibrium constituent concentration in water

CF = Consolidation coefficient

Ch = Cohesion

Cr = Shear resistance

C, = Constituent concentration at mud-water interface

Ci = Concentration of component i








C = Time-averaged constituent concentration

CA = Depth-averaged dye concentration in water at location A

CB = Depth-averaged dye concentration in water at location B

Cc = Depth-averaged dye concentration in water at location C

CD = Depth-averaged dye concentration in water at location D

CE = Depth-averaged dye concentration in water at location E

Cm = Depth-average dye concentration in water over mud trench

Co = Depth-averaged dye concentration in water beyond mud trench

Ct = Average suspended sediment concentration

C = Wave oscillating part of constituent concentration

C' = Turbulent fluctuation part of constituent concentration

ce = Equivalent viscous coefficient

c2 = Equivalent viscous coefficient of fluid mud

c3 = Equivalent viscous coefficient of bed

Ca.5 = Sediment concentration at about one-half water depth at location A

Cb.5 = Sediment concentration at about one-half water depth at location B

co0.5 = Sediment concentration at about one-half water depth at location C

cd.5 = Sediment concentration at about one-half water depth at location D

ceo.5 = Sediment concentration at about one-half water depth at location E

c, = Constant coefficient

D = Diameter of particle or floc

De = Empirical coefficient








Df = Wave-induced diffusivity in fluid mud

Dm = Molecular diffusivity

Di, Di = Diffusion coefficients of component i

Dr = Sediment deposition flux

d = Bed thickness

dl, d2 = Empirical coeffcients

de = Effective grain size

Ei, = Strain tensor

E, = Sediment entrainment flux

E, = Non-dimensional entrainment rate

E'o = Amplitude of E'ij

E',j = Deviatoric components of strain

Ew = Non-dimensional entrainment rate

e = Void ratio

F = Static force

F,, F2, F3, F4 = Normal forces from adjacent particles

Fl2m = Molecular diffusive flux of constituent

F12c = Direct convective flux of constituent

F12d = Indirect convective flux of constituent

Fi2e = Indirect convective flux of constituent associated with entrainment

Fi2p = Particle-bound flux of constituent

F,2s = Indirect convective flux of constituent associated with settling


xvii








Fe = Particle-bound flux of constituent associated with entrainment

FIs2s = Particle-bound flux of constituent associated with settling

FA = Advective flux

FD = Diffusive flux

Fd = Sediment diffusive flux in water

F, = Mass flux of component i

Fp = Sediment deposition flux

Fr = Sediment flux corresponding to the fraction of entrained sediment that is returned

to fluid mud by deposition

F'r = Sediment flux corresponding to the fraction of "settled" sediment that is entrained

into water

F, = Sediment settling flux in water

f = Wave frequency (= o/2rn)

f, f2, f, f4 = Shear forces from adjacent particles

fr = Fraction of sediment exchange between water and fluid mud

fric = Bottom friction coefficient

G = Elastic modulus

GI, G2 = Elastic moduli in standard solid model

Gn = Extensional elastic modulus

G' = Bed rigidity

G' = Elastic energy storage modulus

G" = Viscous energy dissipation modulus


xviii







G* = Complex shear modulus

g = Gravitational acceleration

g' = Effective gravitational acceleration

H = Wave height

Hs = Significant wave height

Hrs = Root mean square wave height

h, = Depth of water layer

h2 = Depth of water and fluid mud

h3 = Total depth of water, fluid mud and bed layers

hk = Thickness of clay particles

I = Light intensity through a fluid medium

Io = Light intensity through clear water

IA = Hue value of Erioglaucine A

IB = Hue value of Rhodamine B

HID = Second invariant of E'j

Jo = Instantaneous compliance

Ji = Diffusive flux of component i

JMa = Mass flux in fluid mud

Jmo = Momentum flux in fluid mud

Jt = Total mass flux in fluid mud

K = Coefficient in relationship between constituent concentration and light intensity

Km = Ratio of floc volume concentration to sediment concentration








KI2c = Convective mass transfer coefficient

Kd = Constituent distribution coefficient

Kn = Neutral mass diffusivity

Kx = Diffusivity in x-direction

K, = Diffusivity in y-direction

Kz = Diffusivity in z-direction

Ki = Diffusivity in z-direction in water

KI2 = Diffusivity in z-direction in fluid mud

Kz3 = Diffusivity in z-direction in bed

K', K" = Characteristic constants in relationship between constituent concentration and

light intensity

k = Wave number

k2 = Equivalent elasticity of fluid mud

k3 = Equivalent elasticity of bed

k, = Convective mass transfer coefficient under current

ke = Equivalent elasticity

ki = Wave damping coeficient or imaginery part of complex wave number

k, = Wave number or real part of complex wave number

k, = Permeability

k, = Yield strength

k'i,(i=8) = Empirical coefficients

LA = Length range represented by flume location A








L, = Length range represented by flume location B

Lc = Length range represented by flume location C

L, = Cohesive resistance

L, = Length range represented by flume location D

LE = Length range represented by flume location E

LEA = Optimal light wave length for Rhodamine B dilution

Li = Inertial force

Lmt = Length of mud trench

L, = Optimal light wave length for Erioglaucine A dilution

Mf = Empirical coefficient

mp = Particle mass

me = Equivalent mass

m2 = Equivalent mass of fluid mud

m3 = Equivalent mass of bed

n = Porosity

ni = Porosity in water layer

n2 = Porosity in fluid mud

n3 = Porosity in bed

nm = Manning's bed resistance coefficient

P = Constituent concentration sorbed on sediment

Po = Initial constituent concentration sorbed on sediment

P, = Constituent concentration sorbed on solids in water








P2 = Constituent concentration sorbed on solids in fluid mud

P3 = Constituent concentration sorbed on solids in bed

P. = Final or equilibrium constituent concentration sorbed on sediment

P" = Maximum concentration of constituent that can be sorbed

p = Deposition probability

Po = Amplitude of wave-induced cyclic pressure

pp = Wave-induced excess pore pressure

p, = Coefficient related to viscoelastic model

p, = Wave-induced cyclic pressure

Q = non-dimensional bouyancy flux

q = Bouyancy flux

q, = Coefficient related to viscoelastic model

R = Radius of clay particle

R2 = Coefficient of determination

Reb = Bottom wave Reynolds Number over rigid bed

Re'b = Bottom wave Reynolds Number over soft bed

Re*b = Bottom wave Reynolds Number over soft bed

Rex = Reynolds Number for current

Re. = Reynolds Number of wave boundary layer

Ri = Richardson Number

Rig = Global Richardson Number

Riw = Wave Richardson Number


xxii








Ri,, = Critical wave Richardson Number for entrainment

Ri, = Critical Richardson Number for entrainment under current

Ri = Rate of reaction of component i

Rr = Relative roughness of mud surface

r = First-order rate coefficient of sorption

r, = Ratio of bottom boundary layer across coefficient, o12c, to this coefficent at static

condition, al2co

S = Sediment concentration

S, = Sediment concentration in water

S2 = Sediment concentration in fluid mud

S3 = Sediment concentration in bed

Sc = Schmidt Number

Scf = Schmidt Number in fluid mud

Sv2 = Sediment volume fraction in mud

S'i = Upper limit concentration for free settling

S*2 = Upper limit concentration for flocculation settling

S*3 = Upper limit concentration for hindered settling

S*4 = Lower limit concentration for negligible settling

S = Depth-averaged sediment concentration

SA = Depth-averaged suspended sediment concentration at location A

S = Depth-averaged suspended sediment concentration at location B

Sc = Depth-averaged suspended sediment concentration at location C


xxiii








SD = Depth-averaged suspended sediment concentration at location D

SE = Depth-averaged suspended sediment concentration at location E

Sm = Depth-average suspended sediment concentration over mud trench

So = Depth-averaged suspended sediment concentration beyond mud trench

St = Average suspended sediment concentration

s = Surface renewal factor

Sao.5 = Sediment concentration at about one-half water depth at location A

sb.5 = Sediment concentration at about one-half water depth at location B

sco.5 = Sediment concentration at about one-half water depth at location C

Sdo.5 = Sediment concentration at about one-half water depth at location D

seo.5 = Sediment concentration at about one-half water depth at location E

T = Wave period

TS = Total suspended sediment mass in flume

Tij = Stress tensor

T'o = Amplitude of T'ij

T'ij = Deviatoric components of stress

U = Mean mixed layer horizontal velocity

u = Horizontal velocity in x-direction

u, = Horizontal velocity in water layer in x-direction

u2 = Horizontal velocity in fluid mud in x-direction

u2max = Maximum horizontal velocity in fluid mud in x-direction

u3 = Horizontal velocity in bed in x-direction


xxiv








u. = Mean longitudinal velocity outside boundary layer

Ub = Maximum wave-induced horizontal velocity just outside wave boundary layer

ue = Rate of downward propagation of interface

u,, = Pore water pressure

u, = Bottom friction velocity

u2* = Characteristic horizontal momentum velocity

u2" = Characteristic horizontal energy velocity

u = Time-averaged velocity in x-direction

Q = Wave oscillating velocity in x-direction

u' = Turbulent fluctuation velocity in x-direction

V = Phase velocity of a high frequency shear wave

v = Horizontal velocity in y-direction

v, = Horizontal velocity in water layer in y-direction

v2 = Horizontal velocity in fluid mud in y-direction

v3 = Horizontal velocity in bed in y-direction

v = Time-averaged velocity in y-direction

V = Wave oscillating velocity in y-direction

v' = Turbulent fluctuation velocity in y-direction

w = Vertical velocity in z-direction

wi = Vertical velocity in water layer in z-direction

w2 = Vertical velocity in fluid mud in z-direction

w3 = Vertical velocity in bed in in z-direction


xxV








w, = Settling velocity of sediment

Wsf = Free settling velocity of fine-grained sediment

= Vertical velocity of flow relative to sediment-water interface

w = Time-averaged velocity in x-direction

S = Wave oscillating velocity in x-direction

w' = Turbulent fluctuation velocity in x-direction

z'c = Fluidization depth

a = Coefficient modulating submerged weight of particle

aI2c = Bottom boundary layer constituent transport coefficient

a12cO = Bottom boundary layer constituent transport coefficient in static condition

ai (i=18) = Empirical coefficients

af = Empirical coefficient

an = Empirical coefficient

a, = Empirical coefficient

Pi(i=1-8) = Empirical coefficients

Pf = Empirical coefficient

Pn = Empirical coefficient

Pv = Empirical coefficient

Yi = Empirical coefficient

y, = Empirical coefficient

, = Shear strain rate

E = Empirical coefficient


xxvi








Es = Specific area of particles

Ex = Current-associated momentum diffusion coefficient in x-direction

Ey = Current-associated momentum diffusion coefficient in y-direction

Ez = Current-associated momentum diffusion coefficient in z-direction

ED = Wave energy dissipation rate per unit area

Ox = Wave-induced momentum diffusion coefficient in x-direction

6, = Wave-induced momentum diffusion coefficient in y-direction

Oz = Wave-induced momentum diffusion coefficient in z-direction

A = Empirical coefficient

Au = Absolute value of velocity difference across mud-water interface

(Au), = Critical value of Au for bottom mud entrainment

Auw = Excess pore water pressure

Ab = Buoyancy jump across mud-water interface

Ap = Density jump across mud-water interface

8 = Boundary layer thickness

81 = Empirical coefficient

8c = Thickness of bottom diffusive layer

8f = Thickness of bottom boundary layer for "film theory"

8i6 = Kronecker delta

E = Empirical coefficient

C = Vertical visplacement of particle

i = Water surface dispalcement


xxvii








Col, Co = Wave amplitudes

C2 = Vertical fluid mud surface dispalcement

C02 = Amplitude of fluid mud surface dispalcement

C3 = Vertical bed surface dispalcement

Co3 = Amplitude of bed surface dispalcement

0 = Tortuosity

K = von Karman constant

p = Dynamic viscocity

pL. = Constant viscosity at the limit of high (theoretically infinite) shear rate

Pa = Apparent dynamic viscosity

Plb = Dynamic viscosity

Pn = Extensional viscosity

Pp = Apparent dynamic viscosity

P' = Dynamic viscosity

p" = Second viscosity

p* = Complex viscosity

v = Kinematic viscosity

ve = Apparent kinematic viscosity

p = Density

p, = Density of water

P2 = Density of fluid mud

p3 = Density of bed


xxviii








p,, p, = Density of water

p, = Specific gravity

o = Total normal stress

o' = Effective normal stress

1 = Shear stress

Tb = Applied bed shear stress

Tcd = Critical shear stress for deposition

Tcm = Critical maximum shear stress for deposition of non-uniform sediment

Tcn = Critical minimum shear stress for deposition of non-uniform sediment

T, = Shear strength

T y = Yield stress

Ya, Tb = Shape functions

= Density stratification correction factor

= Friction angle of sand

() 2, ()2, = Phase shifts

w = Weighting coefficient for wave diffusivity in combined diffusivity of waves and

current

4)c = Weighting coefficient of current diffusivity in combined diffusivity of waves and

current

o = Angular wave frequency

oo = Characteristic resonance frequency

6oo = Coefficient related to tortuosity


xxix













Abstract of Dissertation Presented to the Graduate School
of the University of Florida in Partial Fulfillment of the
Requirements for the Degree of Doctor of Philosophy

SEDIMENT-ASSOCIATED CONSTITUENT RELEASE AT
THE MUD-WATER INTERFACE DUE TO MONOCHROMATIC WAVES

By

YIGONG LI

May, 1996

Chairperson: Dr. Ashish J. Mehta
Major Department: Coastal and Oceanographic Engineering

Constituent release fluxes across the wave-modulated fluid mud-water interface from

bottom sediment into water have been determined through a combination of theoretical

analyses and laboratory experiments.

The dependence of the equilibrium fluid mud depth on characteristic wave and bed

theological parameters is examined for water-bed and water-fluid mud-bed systems.

Theoretical results are compared with data obtained in a wave flume, and an order of

magnitude agreement between measured and predicted fluid mud thicknesses is achieved.

A three-layered, water-fluid mud-bed system is set up for modeling vertical fine-grained

sediment transport. Model results are shown to be in good agreement with laboratory data,

and are also shown to successfully simulate field measurements from two coastal sites.

A vertical constituent transport model, which includes sorption kinetics, is developed

and is combined with the sediment transport model. The total constituent release flux from


xxx








mud under wave action comprises mainly three sub-fluxes including direct convective flux

of the dissolved constituent, indirect convective flux of dissolved constituent and indirect

particle-bound constituent flux. The behavior of the mass transfer coefficient of the direct

convective flux is examined through dimensional analysis, and a Chilton-Colburn type

relation is obtained for determining this coefficient as a function of measurable parameters.

Two clayey sediments are used to prepare bottom mud, and two conservative dyes

are used as constituent surrogates. By calibrating the constituent transport model against

wave flume data obtained for the rate of release of dyes from bottom mud, release sub-fluxes

under wave loading are calculated. The indirect convective sub-flux is found to be an order

of magnitude lower than the directive convective and particle-bound sub-fluxes. However,

the direct convective sub-flux can be amplified several times due to interfacial oscillation,

and the interfacial flux coefficient is found to be related to the Richardson Number. Particle-

bound sub-flux can dominate the constituent release process when significant resuspension

occurs. However, resettling of the sediment flocs and entrapped water tends to considerably

reduce the net release of constituent to the ambient water column. Finally, wave-induced

diffusivity in mud, which controls the rate of upward supply of the constituent to the

interfacial region, is found to be proportional to wave energy dissipation rate per unit volume

of mud, and is shown to be two or three orders of magnitude greater than molecular

diffusion.


xxxi













CHAPTER 1
INTRODUCTION


1.1 Problem Statement


Considerable effort has been made in recent years toward reducing the discharge of

contaminants into fresh water and marine systems. However, these systems, which should

be the beneficiary of an abatement of contaminants, have not always improved as expected.

One reason is that external contaminants have already accumulated in bottom sediments and,

as a result, after the external sources have been removed or reduced, bottom sediments have

become the main sources of contaminants to the water column. Bottom-contaminated

sediments affect the water quality directly via diffusion and convection of the contaminants

into water, or indirectly through resuspension of sediment particles (Fig. 1.1). From Fig. 1.1

we observe that the bottom contaminant released flux can be divided into two categories: (1)

direct flux, due to diffusion and convection and (2) indirect flux, which depends on bottom

sediment suspension. The direct flux has two components: molecular diffusion, which

always exists but is very small compared with the other three fluxes, and convection, which

is due to external wave and/or current action. The sediment suspended-related indirect flux

also has two components: particle-bound flux, in which the contaminant sorbs on sediment

and is transported together with sediment suspension, and indirect convective flux, which

is due to water flow into or out of the bed.













Molecular diffusion Direct co vective flux Indirect coi vective flufarticle ound flux
(due t( eddy and (due to water exchange) (influ nced by
wave-indu ed diffusion) sorptiol /desoprtion)

Dire t flux Indir xt flux
(of dissolve d contaminant) (due to resu pension, including
erosion/entr inment and settling)
Water

Interface Tota: flux
(connective condition between water and bottom mud)
Bottom mud


Figure 1.1 Total contaminant flux and sub-fluxes.



Some examples of bottom contaminated sediment as sources of contaminant to

aquatic systems are summarized in Table 1.1. From this table we note that many types of

contaminants have already accumulated in bottom sediments. Since these sediments

represent an in-place potential contaminant source, quantification of the direct as well as

indirect releases of the contaminant is essential for making an assessment of water quality,

and for predicting further contamination or recovery of aquatic systems (Eadie and Robbins,

1987; Basmadjian and Quan, 1988; Burton, 1991; Reible and Savant-Malhiet, 1993; and

Brownawell and Flood, 1994). For such a quantification, the release fluxes constitute the

crucial boundary or connective conditions at the sediment-water interface in water quality

and contaminant transport models, such as the hydrodynamic and water quality model

WASP5 developed by the Environmental Protection Agency (Ambrose et al., 1991), the

Green Bay integrated exposure model GBTOX for the Great Lakes (DePinto, 1994), and the









3

3-D hydrodynamic, sediment transport and nutrient dynamics models that have been applied

to Lake Okeechobee and Tampa Bay, Florida (Chen, 1994).

Table 1.1 Examples where bottom sediment is the main contaminant source.
Location Contaminants Source

Detroit River, Michigan Metals Theis et al. (1979)

Lake Tarli Karng, Targo Trace metals Hart and Davies (1981)
Reservoir and East Basin Lake,
Australia

Toronto and Hamilton Harbors, Metals Nriagu et al. (1983)
Canada

Ninigret Pond, New York Cadmium and Fluoranthene Di Toro et al. (1989)

Long Island Sound, New York Cadmium Di Toro et al. (1989)
Godavari River Basin, India Heavy metals Biksham et al. (1991)
Guan-Tin Reservoir, China Heavy metals Xian-Chen et al. (1991)

Lake Ontario, Canada PCBs and Mirex Brownawell et al. (1994)

Massachusetts Bay and Heavy Metals, organic pollutants, Butman (1994)
Cape Cod Bay, Massachusetts and sewage contaminants

Lake Okeechobee and Nutrients, e.g., Phosphorus Chen (1994)
Tampa Bay, Florida and Nitrogen

Mikawa Bay, Japan Nutrient salts, e.g., Inoue et al. (1994)
inorganic phosphorus (PO4-P)

Tampa Bay, Florida Trace metals, PAHs, and PCBs Long et al. (1994)

Boston Harbor, Massachusetts Mercury and Lead Manheim (1994)


Among sediments, fine-grained, especially cohesive, materials play a key role in

sediment-associated contaminant transport, because these sediments possess large specific

surface areas and net electrical charges on their surfaces and edges that are essential for the

sorption of contaminants. A variety of factors can influence the release of contaminants from

the bottom sediment to the water column, e.g., hydrodynamic conditions (current velocity,

wave height and frequency, water depth, turbulent mixing, etc.), bottom sediment








4

characteristics (sediment mineral composition, density, theological properties, cation

exchange capacity, organic content, sorptive properties, etc.), suspended sediment

characteristics (sediment mineral composition, flocculation and aggregation, sorptive

properties, etc.), water-sediment exchange processes (settling, deposition, erosion,

entrainment, fluidization, dewatering, etc.), contaminant characteristics (molecular

diffusivity, partitioning properties, etc.), and water properties (pH value, salinity, etc.).

Field evidence and model simulations show that, typically, the top 10-30 cm layer of

bottom mud in the marine and lacustrine environments is active in storing and releasing

contaminants is usually soft and oscillates with water waves (Mehta and Jiang, 1992).

Contaminant fluxes across the sediment-water interface are affected considerably by this

motion and by the thixotropic changes that ensue within the oscillating bed. As a case in

point, Vanderborght et al. (1977) noted that due to bottom stirring the diffusion coefficient

of dissolved silica in the pore water within the top 3.5 cm of the shallow North Sea sediment

was two orders of magnitude greater than that due to molecular diffusion.

For sorptive contaminants, e.g., hydrophobic organic compounds (DDT, PBCs,

PAHs, etc.) or heavy metals (Pb, Cs, etc.), the release flux is also controlled by the reworking

of bottom sediment surface due to sediment entrainment and deposition (Reible and Savant-

Malhiet, 1993 and Brownawell and Flood, 1994). Since the transport processes--settling,

diffusion, deposition and entrainment--are greatly affected by wave loading (Thimakorn,

1983; Maa, 1986; Ross, 1988; Hwang, 1989; Mimura, 1993 and Winterwerp, 1994), waves

can also affect the indirect release of contaminants from the bed through resuspending

bottom sediment, in addition to direct transfer at the interface.








5

Thus, it is evident that contaminant transport models must accurately incorporate the

physical and the physico-chemical mechanisms that operate in the wave-governed dynamical

environment. Typically however, wave-enhanced fluxes are conventionally accounted for

merely by calibrating transport models that are only valid for conditions specified by fixed

beds having constant (time-independent) properties (Berner, 1980). Therefore, given the

considerable importance of properly modeling bottom fluxes for particle-associated

contaminant transport in wave-dominated waters, the need for improving the state of the art

in prediction of fluxes clearly exists.


1.2 Objective. Tasks and Scope


The primary objective of this research is to investigate the role of water waves in

governing the direct and indirect contaminant fluxes across the interface between soft mud

and water layers. Specifically, through modeling and laboratory experiments, the inter-

relationships between wave parameters, contaminant kinetics and mud properties will be

examined for specific contaminant surrogates and bottom muds. This investigation should

also provide an accurate mechanistic description of the connective or boundary condition of

the contaminant mass transfer flux across the wave-modulated water-mud interface for water

quality or contaminant transport models. The specific tasks to accomplish the work were as

follows:

1. Since the mud bed may be fluidized under wave motion, and because once the bed

is fluidized the theological properties and mass transport characteristics of fluid mud can be







6

significantly different from those of the non-fluidized bed, a fluidization model was

developed. Using this model, the fluidization depth under wave motion was predicted.

2. Because aquatic contaminant transport is characteristically associated with sediment

transport, a sediment transport model was set up in a three-layered water-fluid mud-bed

system, which incorporated the effects of fluid mud.

3. Sorption kinetics between sediments and dyes, to be used as contaminant surrogates

in experiments, were determined based on sorption experiments.

4. A sediment-associated contaminant transport model was developed in the three-

layered system. This model incorporated sorption kinetics and was used in conjunction with

the sediment transport model.

5. By calibrating the contaminant transport model against flume experimental data, the

total bottom contaminant releasing flux and its sub-fluxes under wave motions were

determined for various conditions specified by sediment and contaminant compositions and

wave conditions. The relevent coefficients, which determine the magnitudes of the release

fluxes, were obtained for the selected sediments and contaminants under wave motion.

6. An effort was made to explain the results in terms of a phenomenological model

relating the effect of wave and sediment properties on the release fluxes.

To achieve the above tasks, the scope of this study was defined as follows:

1. In the development of the mud fluidization model, only normal stresses were

considered and shear stresses neglected. Thus, this model is only applicable to short period

waves. Also, from this model only the final equilibrium fluidization depth, as would result








7

from steady and sustained wave action, was obtained. The time-dependent process of

fluidization is not predicted by this model.

2. The sediment transport model in the three-layered water-fluid mud-bed system did

not consider sediment exchange between fluid mud and bed, because the fluid mud depth

was considered to be its equilibrium value.

3. Only sorption experiments were carried out for sediments and dyes. The desorption

process were assumed to be the reverse of sorption.

4. Contaminant exchange was studied experimentally by initially inoculating the bottom

sediment with dye and tracking dye release in water under wave loading.

5. The contaminant transport model was calibrated only against laboratory data. The

contaminant surrogates, i.e., were use in the laboratory experiments because their properties

are easily measurable.


1.3 Outline of Presentation


Chapter 2 reviews relevant previous topics and studies on sediment transport, i.e.,

mud rheology, wave-mud interaction, mud fluidization and resuspension of bottom sediment.

Prior investigations on generic sorption models and release of bottom contaminants are also

discussed in this chapter. The fluidization model is developed in Chapter 3. It is compared

with expeirmental data and applied to field, i.e., Lake Okeechobee, in Florida. In Chapter

4, a sediment transport model in the water-fluid mud-bed system is developed. The model

is first calibrated against laboratory data and then applied to field conditions, i.e., the

southwest coast of India and the coast of Louisiana. Chapter 5 describes sorption








8

experiments for dyes, i.e., Rhodamine B and Erioglaucine A, sorbed onto selected sediments,

i.e., a kaolinite and a mixture of kaolinite and an attapulgite. The sorptive properties

between these dyes and sediments are obtained and incorporated in the transport model

described in Chapter 6. In Chapter 6 the sediment-associated contaminant transport model

is developed, which includes sorption kinetics in conjunction with the sediment transport

model developed in Chapter 4. Chapter 7 describes the flume experimental conditions for

bottom contaminant release under wave motion and presents laboratory data for both

sediment and contaminant transport under wave action. To obtain the bottom contaminant

release flux under wave motion, the contaminant transport model developed in Chapters 4

and 6 was calibrated against the flume data, and the results presented in Chapter 7. In

Chapter 8, the release flux and sub-fluxes are compared and correlated to wave conditions

and mud theological properties, and phenomenological explanations are provided for these

corrections. Also in this Chapter, overall study conclusions are presented and

recommendations for future studies are made.













CHAPTER 2
BACKGROUND INFORMATION


2.1 Introduction


The release of conservative contaminants stored in bottom sediments depends on

external hydrodynamic factors, bottom sediment properties and contaminant sorptive

properties. Sediment transport characteristics also play an important role in contaminant

release of contaminants. Thus, theoretical and modeling studies done in the sediment

transport area, i.e., mud rheology, wave-mud interaction, mud fluidization and resuspension

of bottom sediment, are reviewed first in this chapter. Following this review, generic sorption

models and sorptive properties of the selected dyes, i.e., Rhodamine B, Erioglaucine A, used

in this study are described. Field and laboratory experimental observations and previous

studies on the release of bottom contaminants are also described in this chapter.


2.2 Mud Rheology and Wave-Mud Interaction Modeling


The interaction between waves and mud beds is an important issue in understanding

coastal processes. When waves propagate over a mud bed, wave attenuation, energy

dissipation, change in wave kinematics due to corresponding changes in mud properties

under oscillatory loading and bed fluidization, mud mass transport etc. are all due to the

interactions between the wave and bottom mud. Also, vertical sediment transport, due to








10

settling, diffusion, erosion, deposition, entrainment, etc., are influenced by wave-mud

interactions. For modeling these interactions it is necessary to construct a closed set of

equations under wave loading, which include continuity and momentum equations for water

and mud motions. These equations must be solved analytically or numerically. A key step

in formulating the equations is prescribing the momentum equation for mud motion, which

requires a constitutive equation to describe the theological properties of mud.

In contrast to a sandy bed, the mud bed is almost impermeable. Thus, mud is usually

considered as a single-phase continuum. Mud rheology supplies the constitutive equation

to relate the applied load with the mud internal response, which thus describes the macro-

scale behavior of mud under loads resulting from the micro-scale structure of the mud

matrix. Then, substituting the constitutive equation into the equations of motion, the general

dynamic equations for a continuum are obtained.

Thus, the important steps for modeling wave-mud interactions are (1) developing a

mud theological model and (2) solving the closure equations for water and mud under wave

motion with specific boundary conditions.

2.2.1 Mud Rheology

The importance of rheologic properties of cohesive sediment has been recognized in

the coastal seas and estuaries where oscillatory forcing is typically dominant (Mehta, 1991).

Natural cohesive sediments are mainly composed of minerals, colloids and organic materials.

They settle as mud with density determined by the degree of dewatering or consolidation.

The theological properties of such sediments are quite complicated and depend on the

loading shear stress and the reactive shear strain or shear strain rate (Chou,1989) and on the







11

loading frequency (Jiang, 1993), and may in addition be time-dependant (Williams and

Williams, 1992). The general constitutive equation for a continuum is (Malvern, 1969)


Tj = f(Ej) (2.1)


where Ti are the applied deviatoric stresses, Ej are the reactive deviatoric strains and

subscripts i and j denote directions in conjunction with ji, which implies a second order

tensor. Due to the complexity of mud rheology many theological models have been

proposed, as briefly described next.

Linear viscoelastic models

Linear viscoelastic models are widely used at present, and can be generally expressed

as:

M ar N As ,
E p-(Tj) qs -(E ) (2.2)
r= atr s=O at



where superscripts r and s denote orders of partial differentiation, p, and qs are coefficients

related to the selected viscoelastic model, and M and N are the specified maximum

differential orders of the chosen model. Some special and widely used cases of Eq. 2.2 are

as follows:

(1) Elastic material. With po =1, qo = 2G and all other pr and qr equals to zero, the

constitutive equation for an elastic material is (Mallard and Dalrymple, 1977; Dawson, 1978;

Foda, 1989)










Tj! = 2GEj. (2.3)


where G is the elastic modulus.

(2) Newtonian fluid. With po = 1, q, = 2p and all other Pr andq, equal to zero,

the constitutive equation for a Newtonian fluid is (Dalrymple and Liu, 1978; Shibayama et

al., 1986)

Tj = 2pE (2.4)


where p is the viscosity and E. is the deviatoric strain rate, i.e., the time derivative of Ej

with the dot denoting a time-derivative.

(3) Voigt model. With po=l, qo=2G, qt=2p and all other Pr andqs equal to zero, the

constitutive equation for the well known Voigt model is (Fig.2.1a, Carpenter et al., 1973;

Hsiao and Shemdin, 1980; McPherson, 1980; Maa, 1986; Sakakiyama and Bijker, 1989)

Tj; = 2GEj + 2p (2.5)


(4) Maxwell model. With po = 1/2p, p, = 1/2G, q, = 1 and all other p, and q,

equal to zero, the constitutive equation for the well known Maxwell model is (Fig. 2. b)

1 1 .t -,
T--Tj + -20 = E-i (2.6)
2p 2G










2p



4 1 2G 2p
2G

( a) Voigt model (b ) Maxwell model

Figure 2.1 Common two-parameter viscoelastic models.



(5) Jeffrey model. The three-parameter Jeffrey model is an extension of the Voigt

and Maxwell models. Modulating the Voigt model by an additional elastic modulus, 2G,

(Fig. 2.2a), with po = (G +G2)/p2, pP = 1, q0 = 2GG2,/P2, q1 = 2G, and all other p, and

q, equal to zero, the constitutive equation for the Standard Solid model is obtained as

(Keedwell, 1984; Kolsky, 1992; Jiang, 1993)

GI+G2 T + ./ 2GIG2, 2/ /
TI + ji + 2GIEi (2.7)
112 P-2



Constraining the Maxwell model by an elastic modulus, 2G, (Fig. 2.2b), with po = G2/p,2

pl = 1, qo = 2GIG2/p2 and q, = 2(G, +G2) and all other p, andqs equal to zero, the

resulting Jeffrey-Maxwell constitutive equation is

S + G2 / ./ 2GIG2 /
112 Tji + '2Eji + 2(G +G2)Eji (2.8)
P2 P2











2G2 2G2 2[2



L2Gi \A----

2P2 2GI

(a) Standard Solid Model (b ) Jeffrey-Maxwell Model


Figure 2.2 Jeffrey models.

When the external loading is cyclic, e.g., due to water waves, the general constitutive

equation of linear viscoelasticity can be simplified. Assuming that

Tj; = Toexp[-i()t)]
(2.9)
Ejl = Eoexp[-i(wt-8)]


where 0 is the angular frequency of loading, 8 is the phase shift, T/ and Eo/ are the

amplitudes of Tj and El, respectively, and I = (-1)2, the general relation between the

deviatoric stress and the strain is simplified as

N
E q(-iw)s
Tj = E = 2(G'-iG")E. = 2G* Ej (2.10)
M ji (2.10)
E p,(-i )r
r=0



where G* is called the complex modulus, G' is the elastic energy storage modulus and G" is

the viscous energy dissipation modulus. As an alternative to Eq. 2.10, the general relation

between the deviatoric stress and the strain rate can be obtained as










N
Sq%(-i")s
T ,-- q- ;= 2( p+ip.ll' = 2p* j/ (2.11)
Ti M (2.11)

r=O



where p* is called the complex dynamic viscosity, p' is the dynamic viscosity and p" is

called the second viscosity. Accordingly, the different theological models described can be

obtained as follows:

(1) Elastic material,

P = Pp ; i" = 0 (2.12)


(2) Newtonian fluid,


p' = o ; pH = G (2.13)


(3) Voigt model:


pt = p ; Pl G (2.14)


(4) Maxwell model,


G G )
_P = //w (2.15)
2 +( G 2+( G)










(5) Standard Solid model,


G\ G, (G1+G2)G2 +W2
G W 2
P +G 2 2 2 (2.16)
G G, + +G,
P2 P2


(6) Jeffery-Maxwell model,


G 1GIG 2
G ) i +o2 (G+G2)
G 2 ItI
/ .= 2 [ 2 2 (2.17)
G G2 2
I2 2 2


As mud rheology is complicated, none of the above models can describe mud

response under all types of loading conditions. However, for the case of mud response to

cyclic loads (Eqs. 2.10 and 2.11), a practical way to characterize mud rheology is by carrying

out a dynamical oscillatory test (Chou, 1989; Jiang, 1993). Through this test the complex

modulus, G*, or the complex dynamic viscosity, pI*, can be obtained under specific

conditions for practical use, without considering a particular model describing mud rheology.

Thus, for example, Chou (1989) related the complex modulus, G*, with strain amplitude by

using controlled strain rheometry. Then, he incorporated the resulting strain-dependant

rheologic model into his wave-mud interaction model to predict mud response to wave

motion. Jiang (1993) related the three parameters of the standard solid model to wave

loading frequency and then obtained the complex dynamic viscosity, P*, which also therefore

depends on the loading frequency, for his wave-mud interaction model. Such









17

experimentally based relations will continue to play an important role in modeling mud

rheology, before a fuller theoretical understanding of mud rheology is obtained.

Theoretically, predictive accuracy can be increased by introducing more and more

elastic/viscous elements used for modeling mud rheology. However, the more the elements

in a model, the greater the number of coefficients that must be determined. Thus, greater

complicated experimental procedures are required, which in turn limit the use of large-

element models. On the other hand, some nonlinear properties, e.g., plasticity, time-

dependant properties, etc., are often important in mud theological response to loading. As

a result, some nonlinear viscoelastic models have also been proposed for mud rheology.

Nonlinear and Time-Dependent Models

The three-dimensional structure of soft mud beds can resist small shear stresses at

rest. To account for this resistance, viscoplastic models have been used (Engelund and Wan,

1984; Suhayda, 1986; Mei and Liu, 1987; Tsuruya, 1987; Liu and Mei, 1989; Shibayama et

al., 1990). For small strains, the constitutive equation for a viscoplastic material can be

expressed as (Malvem, 1969)


T,= 2.p + k E (2.18)




where p p is the apparent viscosity, ky is the yield strength and IID is the second invariant of

E'. For the one-dimensional condition, Eq.2.18 can be simplified to (Wilkinson, 1960)
Ji"


T = Ty + Lp /


(2.19)








18

where r is the applied shear stress, Ty is the yield stress and ? = au/az. Here u is the

velocity in the same direction as T.

For the commonly found shear-thinning behavior of mud, i.e, one in which the

apparent viscosity decreases as the shear strain rate increases under increased shear stress

loading, mud can be modeled by a power-law equation (Sisko, 1958; Feng, 1992)


T = t. + c" (2.20)



where the apparent viscosity, pp, = u + cY"-', p-is the constant viscosity at the limit of

high (theoretically infinite) shear rate, c is a measure of the consistency of the material and

n < 1 is a mud-specific parameter.

James et al. (1987) conducted creep-compliance tests for illitic suspensions by using

a combination of an applied stress rheometer and a miniature vane geometry. They found

the instantaneous compliance, Jo = y/t, to be related to the applied shear stress. The

material was predominantly elastic at low shear stresses and was essentially viscous at high

shear stresses. Chou (1989) measured soft mud theological properties composed of a

kaolinite and a montomorillonite and found that the storage modulus, G', and the loss

modulus, G", changed with the shear strain amplitude.

By using shear wave rheometry, Williams and Williams (1992) measured the G' and

G" values of mud under oscillatory loads, and found that G' and G" changed with the wave

loading time, thus quantitatively demonstrating that mud has a time-dependant theological

response. Mehta et al. (1995) correlated the phase velocity of a high-frequency shear wave

in a mud bed with bed rigidity. The fall in the velocity, starting with an undisturbed bed








19
under monochromatic wave, indicated that the bed rigidity decreased as a result of bed

fluidization under wave motion. Thus, the bed had a time-dependant theological response

to wave motion.

2.2.2 Wave-Mud Interaction Modeling

Prior to the late 1950s, wave energy dissipation was mainly considered in connection

with bottom friction, percolation, wave refraction and shoaling. Brestschneider and Reid

(1954) presented graphic solutions for obtaining wave attenuation by these factors.

However, it must be pointed out that a mud bottom is usually not rigid and is almost

impermeable to water flow. The dissipation of propagating wave energy over the mud bed

is mainly due to internal friction within mud, which is characterized by mud rheology and

wave loading.

Based on Biot's (1941) 2-D, nonporous, perfect-elastic soil theory, Mallard and

Dalrymple (1977) modeled mud bed as an elastic material to study soil stresses and

displacement under wave motion. In their modeling, soil inertia was neglected and there was

no energy dissipation since mud viscosity was not included. Taking soil inertia into account,

Dawson (1978) also modeled mud as an elastic material. However, wave energy dissipation

was not considered.

An early theoretical and laboratory study on the effects of a nonrigid, impermeable

bottom on the surface wave was carried out by Gade (1958), who modeled the water layer

as an inviscid fluid overlying a viscous fluid layer of greater density. Solution for the

shallow water, single harmonic wave indicated that wave height decayed exponentially with

distance traveled, and that wave energy dissipation over the soft bottom was substantially









20

greater than that over a rigid bed. Dalrymple and Liu (1978) developed a theory for a small

amplitude linear wave propagating in a two-layered viscous fluid system. Both the governing

equations of continuity and motion and the surface, interface and bottom boundary

conditions were linearized, and an analytical approach was used for solving the equations.

The results showed that most of the energy dissipation was due to internal friction within the

soft mud as a result of high viscosity, and that extremely high wave attenuation rates are

possible when the thickness of the lower layer is of the same order as the internal boundary

layer thickness. Based on Dalrymple and Liu's work and boundary layer approximation,

Jiang and Zhao (1989) and Jiang et al. (1990) developed analytical approaches for calculating

wave attenuation for viscous mud beds under shallow water solitary and cnoidal waves.

These modeling studies included the nonlinear properties of waves in shallow water.

By considering both the viscous and the elastic properties, Hsiao and Shemdin (1980)

and McPherson (1980) independently applied the Voigt model to represent mud rheology and

used analytical approaches to solve for the assumed inviscid water wave propagating over

a linear viscoelastic bed. McPherson introduced a viscoelastic parameter, ve = */p (see Eq.

2.11), which is essential for the formulation of the problem based on the viscoelastic

assumption. For the Voigt model, ve = p/p +iG/cop (see Eq. 2.14). McPherson's results

showed that depending on the elasticity and the viscosity of the sea bed, wave attenuation can

be of the same or a larger order of magnitude than that due to bottom friction or percolation.

Hsiao and Shemdin compared their results with field measurement reported by Tubman and

Suhayda (1976) in East Bay, Louisiana, and obtained reasonable predictions. Considering

mud density increases with depth, a multi-layered Voigt model was used by Mehta and Maa








21

(1986) to model mud bed motion under a linear wave. The calculated water-mud interfacial

bed shear stresses was found to be larger than those obtained by assuming mud to be rigid.

Chou (1989) developed a three-phased viscoelastic model for mud rheology, and

under linear water wave motion a four-layered wave-mud interaction model was set up. The

depths of the second, viscous layer, and the third, viscoelastic layer, layers were determined

as part of the solution through an iterative technique. The model showed that the mud

fluidization depth and wave attenuation rate increase with wave height for a partially

consolidated mud. Using controlled-stress rheometry, Jiang (1993) modeled mud as a

Standard Solid (see Eq. 2.16). An analytical solution and laboratory tests were used to study

wave-mud interaction, wave attenuation and mud mass transport. The modeling results

compared favorably with laboratory experimental data and with field data from Lake

Okeechobee in Florida and the southwest coast of India.

Besides linear viscoelastic models, some nonlinear viscoelastic, viscoplastic and

other models have also been used in wave-mud interaction modeling and mud behavior in

general. Engelund and Wan (1984) used the viscoplastic model to study the instability of

hyperconcentrated flows. They claimed that the Bingham model was valid for the

description of the instability of the fluid surface elevation.

Mei and Liu (1987) considered bottom mud to be viscoplastic. The special case of

a shallow mud layer under the action of long waves propagating in water was considered.

It was found that under certain conditions the dynamics of a plug flow layer, unsheared in

the domain with stresses below the yield stress, contributed measurably to wave attenuation









22

over a long fetch. In particular, as waves propagated mud motion could change from

continuous to intermittent.

Tsuruya et al. (1987) extended Dalrymple and Liu's (1978) viscous-fluid model to

a Bingham fluid. The equivalent viscosity, Pa which takes non-Newtonian mud rheology

into account, was defined as

au au
T a = t0 + Pb (2.21)
tz 8z


where to is the yield stress, Pb is the dynamic viscosity and the apparent dynamic viscosity


P + Pb (T > To)
Pa u (2.22)
az


Thus, the Bingham fluid was introduced into the Newtonian equation of motion in an

approximate fashion. Laboratory tests on wave attenuation and mud mass transport were

also conducted.

Using the viscoplastic Bingham model for a thin mud layer under solitary waves, Liu

and Mei (1989) analytically solved the wave-mud interaction problem through a boundary

layer approximation. They found that wave dissipation is due to the bottom mud shear layer

and the turbulent interfacial stress. Continuous to intermittent mud motion could be

predicted from this model.

Studying linear wave propagation over a soft mud, Shibayama et al. (1990) modeled

mud as a viscoelastic and/or viscoplastic material depending on the loading shear stress.

Fluid mud was assumed to be viscoelastic when the stress was less than the yield stress, and








23

was considered to be viscoplastic when the stress exceeded the yield stress. The resulting

numerical model could predict mud mass transport under wave action.


SMWL



Mobile Suspension
Entrainment Settling
SFluidization Dewatering
.^.1 A----L------------.
LutoclineFluid Mud
-- --------------
^^ -~" -- ---- -^ -----------
Deforming Bed

Stationary Bed


Figure 2.3 A typical wave-mud system (after Hwang, 1989)



2.3 Mud Fluidization and Fluid Mud


The interactions between unsteady flows and soft bottom mud are not well

understood at present, especially when a fluid mud occurs at the bottom. Fluid mud is a

concentrated sediment slurry having non-Newtonian theological properties. It may be

generated by rapid deposition of suspended sediment or by fluidization of the mud bed by

waves (Winterwerp, 1994). In Fig. 2.3, a qualitative description of the mud-water system

is given, in which u is the horizontal wave orbital velocity. The bulk density of the water-

mud mixture, p, varies from the water surface to the bed bottom. A sharp density gradient,

or lutocline (Parker and Kirby, 1982), separates the upper column suspension from fluidized















24

mud below. The bed just below fluid mud tends to undergo deformation. Below the level

at which the depth of penetration of the wave orbit ends, the bed remains uninfluenced by

wave motion.


Mean Water Surface

Mobile Suspension
S\ Fluid Mud Surface (Lutocline)
S' = 0 Fluid Mud
Bed Surface

Wh "% % w Bed



STRESS

Figure 2.4 Schematic of instantaneous stress profile in a wave-mud system
(after Mehta et al., 1994).



An instantaneous view of the stress profiles in the mud-water system is shown

schematically in Fig. 2.4, in which oh is the hydrostatic pressure, Au, is the wave-averaged

excess pore pressure, o' is the wave-averaged effective normal stress, uw is the pore pressure

and the total stress, a = uw + o = oh + Auw + Considering the time-variation of the

normal stress in the bed at a given point, as the excess wave-mean pore water pressure builds

up gradually under wave motion, the effective stress reduces accordingly. When the pore

water pressure equals the total pressure at some elevation, i.e. when the effective normal

stress is zero, the bed at and above this elevation is considered to be fluidized (Ross, 1988;










25

Feng, 1992). Thus, fluid mud is actually supported by water and has fluid-like properties,

while the non-fluidized bed retains a structured sedimentary matrix.

Because the theological properties and the mass transport characteristics of fluid mud

can be significantly different from those of the non-fluidized bed, fluid mud must be modeled

separately from the bed. Therefore, to investigate water-mud bed interactions, once the bed

is fluidized, a three-layered water-fluid mud-bed system must be set up (see Fig. 2.5).




Water layer DifBia.t s-tl 8

Wata-fluid Tedterfutcs E et f Depotsiion

Fluid mud layer
Fluid mud-bed Interfa FdizitionI Dewatetin

Bed layer
Bed bottom

Figure 2.5 Three-layered water-fluid mud-bed system and vertical sediment transport
processes under waves.



To investigate vertical mass transport in the three-layered system, several mass flux-

associated processes must be determined quantitatively. In the water layer, the sediment

settling velocity and the buoyancy-stabilized diffusivity must be specified. The entrainment

rate of fluid mud and the deposition rate of sediment onto the surface of fluid mud must be

modeled. To determine the fluid mud layer thickness and the mass fluxes of sediment across

the fluid mud-bed interface, fluidization characteristics of the bed and dewatering of fluid

mud by consolidation must be understood.









26

Fluid mud thickness can affect both the velocity distribution in the water column

through wave-fluid mud interaction (Jiang, 1993), and mass exchange between water and

bed. However, a fully operational model to predict fluidization under waves has not yet been

developed. Roberts (1993) used the three-layered system to develop a two-dimensional

horizontal model to predict fluid mud movement under storm waves in the coastal zone. The

thickness of fluid mud was assumed to be equal to the wave boundary layer height by way

of the argument that the water-fluid mud interface coincides with the top of the wave

boundary layer. However, this assumption is not always appropriate, since in general the

interface can rise above the height of the boundary layer or occur below the latter. By

measuring the pore and total pressures within the bed under wave motion in a laboratory

flume, Feng (1992) developed an empirical formula for determining fluid mud thickness.

Combining the experimental data of Feng (1992) and the theological properties of mud

measured by a miniature shearometer (Williams and Williams, 1992), Mehta et al. (1994)

also developed an empirical formula to predict time-varying fluid mud thickness during

fluidization. These two empirical relations are limited to the types of sediment and wave

conditions used in the experiments for which they were derived. Therefore, to determine the

necessary coefficients for other sediments or wave conditions, additional experiments must

be carried out.

For modeling the depth of fluidization, Foda et al. (1993) applied a wave-bed

interaction model incorporating the assumption that the viscoelastic properties of mud are

dependent on the wave-induced strains within the bed. This model can only predict the final

equilibrium fluidization depth, which is actually a time-dependent process starting with a bed








27

over which wave motion commences. By using a miniature rheometer to measure the phase

velocity, V, of a high-frequency shear wave in a mud bed and then correlating V with bed

rigidity, G', Mehta et al. (1995) obtained the empirical relation

G r(t) [V(t)]2 2(2.23)
G = -t ) exp(-at) (2.23)
G (O) LV(0)



where a, and P, are empirical coefficients dependent on bed theological properties and the

wave characteristics. It was found that the trends of increasing measured fluid mud thickness

with time, d(t), were quantitatively in agreement with the trend of decreasing V(t) and were

empirically expressed as

dr(t) = M[1 -exp(-at ')] (2.24)


whereM, a, and P, are empirical coefficients. However, a theoretical explanation for Eq.

2.24 was not provided. In fact, since the fluidization process is not well understood, in the

present development the fluid mud layer will be considered to be of the final equilibrium

thickness.

Dewatering is the process by which fluid mud consolidates and the bed structure is

rebuilt. Experimental measurements of Feng (1992) and de Wit (1994a, 1994b) indicate that,

as long as wave motion continues, fluid mud can be maintained and may not dewater. Since

in the present case only the equilibrium thickness of fluid mud is to be considered, the

dewatering process will not be examined. Thus, no portion of fluid mud will be considered

to dewater to become part of the bed layer. For the same reason, no bed sediment will be









28

fluidized. Therefore, sediment mass transport across the interface between the fluid mud and

the bed will be neglected and the fluid mud-bed interface will be considered to be fixed in

elevation.


2.4 Processes Governing the Vertical Structure of Suspension


Referring to Fig. 2.5, in the water layer settling and upward diffusion of the

suspended sediment determine the vertical distribution of sediment concentration. The

entrainment rate of fluid mud or bed and the deposition rate of suspended sediment onto the

surface of fluid mud or the bed govern sediment exchange between the water and fluid mud

or bed.

2.4.1 Settling

The settling velocity of cohesive sediments strongly varies with the concentration in

suspension (Mehta, 1988a). A descriptive plot is shown in Fig. 2.6 for the relationship that

is typically found between the settling velocity, ws, and the suspended sediment

concentration, S. Also shown is the variation of the corresponding settling flux, F, = w,S.

The settling velocity regime can be divided into three sub-ranges depending on the

concentration and the mode of settling, which can be free settling, flocculation settling or

hindered settling.

Free settling occurs in the very low suspension concentration range, when S < S,

(see Fig. 2.6). In this range the particles or flocs settle independently and the settling velocity

is not a function of suspension concentration. For cohesive sediments, the upper








29

concentration limit, S 1, is considered to be in the range of 0.1 to 0.3 g/1 (Mehta, 1988). The

settling velocity in the free settling range is usually assumed as a constant, i.e.:


w = ws = a S = const
S f a I


(S < S *)


where at and P, are coefficients which will be explained next.





i4 Settling Flux

O
o
0 n
SWo ......----- ----




w, = Const. Settling Velocityl

I I
W Wf F o
to Free Flocculation Settling I Hindered
o4 settlmgi ` I Settlipg


(2.25)


Log(CONCENTRATION)


Figure 2.6 A schematic description of settling velocity and flux
variation with suspension concentration (after Hwang, 1989).



Flocculation settling occurs in the middle suspension concentration range specified

by S < S < S In this range increasing concentration leads to increasing interparticle

collision and enhanced particle aggregation. Thus, the settling velocity increases with

concentration due to the formation of stronger, denser and larger flocs or aggregates. The

typical relationship between the settling velocity and suspended sediment concentration is











Ws = a1S P S; < S < S (2.26)


where pi is 4/3 theoretically (Krone, 1962), although the actual value typically varies

between about 0.8 and 2 (Mehta, 1988a). The proportionality coefficient, bn, can vary by

an order of magnitude depending on sediment composition and the flow environment.

Hindered settling occurs in the high concentration range, when S > S ;. In this range,

the occurrence of an aggregate network hinders the upward transport of interstitial water.

Thus, w, decreases with increasing S ( Kynch, 1952). A widely accepted relationship for the

settling velocity as a function of concentration was developed by Richardson and Zaki (1954)

w, = ws( -la/ S)P2 (S > S) (2.27)


where w0s is the initial or reference settling velocity, a/' is a coefficient depending on the

sediment composition and 32 = 5. Above the concentration S4*, the settling flux is

negligible.

Hwang (1989) measured the settling velocity of sediments collected from Lake

Okeechobee in Florida, and parameterized the effects of flocculation and hindered settling

on the settling velocity by way of a nonlinear formula dependent on the sediment

concentration, and expressed as

a S1
w (2.28)
(S 2 + Y)2








31

where a,, PI yi and 8, are empirical constants which must be experimentally determined for

different sediments.

2.4.2 Diffusion

The rate of upward diffusion of suspended fine-grained sediment is governed by the

mass diffusivity determined by hydrodynamic forcing and also by density stratification,

which tends to damp diffusion. The diffusivity, KI, is usually expressed as the product of the

neutral mass diffusivity, Kn, and the density stratification correction factor, D (Rossby and

Montgomery, 1935; Munk and Anderson, 1948; Ross, 1988), i.e.

Kz = K, D (2.29)



The most commonly applied expression of the vertical variation of the neutral mass

diffusivity for turbulent unidirectional flow was developed by Rouse (Vanoni, 1975).

Following von Karman's assumption of a linear shear stress distribution with depth and a

logarithmic velocity profile, the neutral diffusivity is expressed as


Kn = Ku*z 1- (2.30)




where K is von Karman's constant, u, is the friction velocity, h is the water depth and the

coordinate z is upward originating from bed surface. However, under wave motion, the

diffusivity becomes complicated and has not been fully parameterized thus far. By analogy

with the mixing length theory in unidirectional flows, Homma et al. (1962) gave a plausible

expression for the wave diffusivity. To overcome the shortcomings found in the derived








32

expression, Homma et al. (1965) modified the expression by introducing a mixing length

following the von Karman hypothesis. The resulting neutral wave diffusivity under the linear

waves was expressed as


K H sinh3k(h+z) (2.31)
Sksinhkh cosh2k(h+z)




where P2 is a constant, H is the wave height, o is the wave frequency and k is the wave

number.

Hwang and Wang (1982) summarized the models available for the turbulent diffusion

coefficient outside the wave boundary layer and indicated that Prandtl's mixing length theory

may not be applicable due to the large scale of wave motion. They assumed that the wave

diffusivity is proportional to the vertical velocity component and the orbital radius of the

water particle in the vertical direction. Using the linear wave theory, the expression for wave

diffusivity was obtained as

K = 2H 2 sinh2kz
Kn = a2H' o- (2.32)
2 sinh2kh



where a2 is a constant. From the concept based on energy in a turbulent field, Thimakorn

(1984) expressed the eddy diffusivity as


Kn = 0.885 H -2 n (2.33)
sinh3kh










33

which is similar to Hwang and Wang's expression, with a2 = 1.77/sinhkh.

Stratification due to density variation in suspension can measurably alter the vertical

momentum and mass mixing characteristics. In the case of stable density stratification in

which the density decreases upward, vertical diffusion is impeded by the stabilizing

gravitational force of sediment suspension acting against the destabilizing force due to fluid

shear. The local gradient Richardson number, Ri, is usually used as a measure of stability,

and is defined as

ap
Ri -g az
p ( (2.34)
iaz



where g is the gravitational acceleration, p is the density and z is positive upward. Positive

values of Ri indicate stable stratification, negative values indicate unstable stratification and

Ri = 0 implies a neutral condition. The greater of the positive value of Ri, the greater the

suppression of vertical diffusion.

A number of models for the density stratification correction factor, D, in Eq. 2.27,

and therefore for stratified diffusivity, have been proposed. One of the most frequently used

expression was developed by Munk and Anderson (1948), which is


K = Kn(1 +33Ri)al (2.35)


where a3 and 33 are empirical coefficients and, typically, a3 varies from -0.5 to -2.0 and P3

varies from 0.3 to 30 (Rossby and Montgomery, 1934; Holzman, 1943; Munk and Anderson,







34

1948; Nelson, 1972; French, 1979; French and McCutcheon, 1983) depending on sediment

composition and the flow environment. Thus, the diffusive flux, Fd, can be expressed as


Fd = -Kz -Kn(1 + Ri)a3 a- (2.36)
z z z

Without the effect of buoyancy stabilization, Ri = 0 and Kz = Kn, so that the diffusive flux

is linearly proportional to the vertical concentration gradient, aS/az. However, since the

local gradient Richardson number, Ri, is proportional to ap/az a 9S/az, the stratified

diffusivity, KI, is inversely proportional to the vertical concentration gradient with a3 < 0.

Thus, nonlinearity between the diffusive flux, Fd, and aS/az develops when gravitational

stability is considered. Also, from the theoretical results of Eq. 2.34, the diffusivity flux

initially increases with low values of aS/az, reaches a maximum and then slowly decreases

with high values of aS/az. The formation of the lutocline is strongly related to the nonlinear

dependence of Fd on aS/az (Eq. 2.34) (Ross, 1988; Hwang, 1989; Costa, 1989; Scarlatos and

Mehta, 1990).

Ross (1988) and Hwang (1989) used Eqs. 2.30 and 2.34 in their vertical fine-grained

sediment transport modeling. Model results were found to be in agreement with laboratory

data, and with field data from the Severn Estuary and tributaries, United Kingdom (Kirby,

1986; Kirby and Parker, 1977) and from Lake Okeechobee in Florida (Hwang, 1989). Also,

lutoclines could be simulated with the models.










2.4.3 Deposition Rate

The deposition rate of suspended sediment onto fluid mud surface can be expressed

as the product of the settling rate of sediment near the mud surface and the probability of

deposition (Krone, 1962; Mehta, 1988b). Thus, deposition rate, Fp, is expressed as

Fp = -wSPI mud surface (2.37)



where p is the deposition probability. The concept of this probability implies that deposition

occurs through the sorting of suspended sediment aggregates, which in turn occurs because

of the high rates of fluid shear near the bottom. When the aggregates are strong enough to

withstand the near-bed shear stress, they stick to the bottom mud; if not, they are disrupted

and resuspended.

Krone (1962) first related the deposition probability to the relative shear stress as

0 (Tb Tcd)

p = b < (2.38)
1- (b



where Tb is the bed shear stress and "cd is the critical shear stress above which no deposition

occurs. This stress typically varies from 0.04 0.15 Pa.

Mehta (1986) and Mehta and Lott (1987) studied nonuniform sediment deposition

and defined the critical shear stress for deposition of such sediment. With -rm and Tc defined

as the maximum and minimum values, respectively, of the critical shear stress for deposition,

tci, for tb > cm no initially suspended sediment can deposit, while for Tb < cn the entire of










36

suspended material will eventually deposit. For on < Tb < cm a fraction of the initially

suspended sediment for which li < Tb will not deposit, while the remainder will finally

deposit at steady state. Using this approach the instantaneous concentration variation with

time can be predicted depending on the initial suspension concentration, settling velocity,

sediment size distribution and the flow condition.

Sanford and Halka (1993) investigated sediment resuspension in Chesapeake Bay and

found that the resuspension model with the assumption of no critical stress for deposition

described the field data better than one including the critical stress. They suggested that

deposition always occurs, and is proportional to the near bottom suspension concentration.

Thus, even at steady state when the suspended sediment concentration is constant, sediment

exchange between the water column and the bed exists. The deposition rate in this case is

expressed as


Fp = -wsS mud surface (2.39)


which is a special case of Eq. 2.37 with the deposition probability equal to one.

2.4.4 Entrainment

The problem of erosion of cohesive sediments has been extensively investigated

(Grissinger, 1966; Kelly and Gularte, 1981; Parchure and Mehta, 1985; Sheng, 1986; Maa

and Mehta, 1987; Shaikh et al, 1988), with different types of deposited or remolded clay beds

under current or wave motion, in fresh or saline water. Erosion of mud bed is due to: (1)

frictional, gravitational and cohesive bonding forces of bed being exceeded by the

hydrodynamic erosive force, which causes bed surface erosion, and (2) the bed bulk shear








37

stress being exceeded by the flow-induced shear stress,.which causes mass erosion (Mehta,

1986).

In the above context it should be noted that the mechanism by which fluid mud is

entrained by shear flow differs from that governing the rate of erosion of the settled mud

having a structured matrix (Mehta and Srinivas, 1994 and Kranenburg, 1994). Entrainment

is due to the breakup of the fluid mud-water interface, which is characterized by the ratio of

the destabilizing factor, the mechanical mixing energy, and the stabilizing factor, the

potential energy stored in density stratification (Scarlatos and Mehta, 1993 and Mehta and

Srinivas, 1993).

Kato and Phillips (1969) applied a constant shear stress, T = p u at the surface of

an initially linearly stratified fluid in an annular flume. This resulted in the development of

an upper homogeneous layer and a lower stratified fluid with an interfacial buoyancy jump

Ab. They arrived at the expression


u.
E, =_e=K1Ri,-7 (2.40)




where E, is the non-dimensional entrainment rate, ue is the rate of downward propagation of

the interface, u* is the friction velocity and the Richardson Number, Ri, = hAb/u2, and h

is the depth of the upper homogeneous layer. Moore and Long (1971) ran two-layered

experiments in a race-track shaped flume with density and velocity profiles being uniform

in the longitudinal direction. Over the range of the global/overall Richardson Number, Ri ,








38

studied, they found that the non-dimensional buoyancy flux, Q = q/Ab (2AU), was related

to the overall Richardson Number according to

Q ~ Rig-' (2.41)



where q is the buoyancy flux, 2AU is the velocity difference between the two layers and

Rig = lIAb/(2AU), in which H is the total depth.

In the field, Bedford et al. (1987) measured sediment entrainment in Long Island

Sound, and examined its dependence on the bed shear stress, the Reynolds stress, and the

turbulent and wave kinetic energies. Only the time-patterns of turbulent and wave kinetic

energies correlated with the entrainment time pattern.

Scarlatos and Mehta (1993) approximated the mud-water system by a two-layered,

slightly viscous, horizontal system with water flowing over fluid mud. By introducing a

slight disturbance along the interface, the vortex sheet initially developed a wave-like pattern,

typical of Kelvin-Helmholz instability. Then the vortex sheet stretched, folded and

eventually caused a thickening and vigorous mixing of the interface. It was demonstrated

that the dynamic behavior of the vortex sheet is controlled by the velocity and density

gradients across the interface.

Mehta and Srinivas (1993) examined the entrainment behavior of fluid mud subjected

to turbulent shear flows based on theoretically analyzing the turbulent kinetic energy

equation and using experimental data. A non-dimensional formula for the entrainment rate

dependent on the global Richardson Number was obtained as









39

E = AeRig--DeRig (2.42)



where E = ue/U, Rig = hAb/U2, Ab is the buoyancy jump across the water-fluid mud

interface, U is the mean mixed layer velocity, h is the mixed layer depth, and Ae and De are

experimentally determined coefficients. The first term on the right side represents the

interaction between mechanical mixing energy and potential energy stored in density

stratification. The second term arises from influences of particle settling, cohesion, viscosity

difference between mud and water etc. It should be noted that according to Eq. 2.40, at low

values of Rig the upward flux of sediment mass is proportional to the cube of the mean

mixed layer velocity. In contrast, the rate of erosion of cohesive bed depends on U2 in

turbulent flows (Partheniades, 1965; Mehta, 1989).

Winterwerp (1994) carried out experiments on the entrainment of soft mud layers in

an annular flume and also found the entrainment rate of fluid mud to be governed by the

global Richardson number. The non-dimensional entrainment rate, E. = uc/u,, was

correlated with Ri.-1/2 for small Ri. and with Ri,-' for large Ri, where Ri, = hAb/u2.

Kranenburg (1994) derived an entrainment model for fluid mud by integrating the

equation for turbulence kinetic energy over the mixed layer and introducing some modeling

assumptions. Two basic conditions for entrainment were considered. In case 1, the water

layer was selected to be the turbulent mixing layer and fluid mud entrained into water layer.

In case 2, turbulence was considered to be produced primarily in the fluid mud layer due to

the shear stress at the bottom of the fluid mud layer. Water entrained downward into fluid








40

mud layer increased the fluid mud depth with time. Such behavior has also been reported

in the field by Wolanski et al. (1988) and Le Hir (1994).


2.5 Sorption Models


Sorption processes include adsorption, chemisorption, absorption and ion exchange

(Fetter, 1992). Adsorption is the process by which a solute (sorbate) clings the solid

sorbentt), i.e., sediment, surface. Chemisorption occurs when the solute is incorporated on

a solid surface by a chemical reaction. Absorption describes the process that the solute goes

beyond the solid surface and diffuses into the porous interior compartment of the solid. Ion

exchange is the process that charged solutes exchanges with ion on solids surface. From a

practical point of view the important aspects are the removal of the solute from solution to

sorb onto or into solid, or the release of solute from solid into solution, irrespective of the

details of process mechanics. If the rate of sorption is much faster than advective-diffusive

transport rate of solute, the process can be described by an equilibrium sorption isotherm.

If the rate of sorption is slow or of the same order of magnitude as advective-diffusive

transport rate of solute, the process must be described by a kinetic sorption model. Some

sorption processes may be more complicated and must be described by more complicated

models which may include multi-step reaction and/or diffusion steps (Wu and Gschwend,

1986).

2.5.1 Equilibrium Sorption Isotherm

Linear Sorption Isotherm









41

The simplest and most widely used equilibrium sorption isotherm is the linear

sorption isotherm which is given by a linear relationship between the solute concentration

in solution, C, and sorbed on solid, P

P = KdC (2.43)



where Kd is the distribution coefficient, which is a measure of the retention of solute by the

solid.

The linear isotherm model has been used frequently to describe the sorption of

radioactive materials by soils (Burkhoider, 1976; Van De Pol et al., 1977). Davison et al.

(1968), Scott and Phillips (1972) and Sleim et al. (1977) have employed Eq. 2.43 in studies

of the movement of herbicides in the soil column. Lai and Jurinak (1972) and Lai et al.

(1978) have used the linear isotherm for the sorption of metals, i.e. Na and Mg2', on soils

in their studies of cation sorption during convective-diffusive flow through soil. Overman

et al. (1976) have used this isotherm in their study of phosphorous transport. Since the linear

isotherm can be conveniently incorporated into solute transport models and is easily

determined, it has also been used in a number of studies to predict the rate of movement of

solute fronts (Anderson, 1979; Faust and Mercer, 1980 and Srinivasan and Mercer, 1988).

However, a limitation of this isotherm is that it does not include any upper limit to the

amount of solute that can be sorbed onto the solid.

Freundlich Sorption Isotherm

A more general equilibrium sorption isotherm is the Freundlich isotherm, which is

defined by a nonlinear relationship











P = k'lCN (2.44)



where k', and N are constants. When k', = Kd and N = 1, Eq. 2.44 reduces to the linear

sorption isotherm (Eq. 2.43).

The Freundlich isotherm has been widely applied to model the sorption of various

metals such as copper, zinc and cadmium by Sidle et al. (1977), molybdenum by Jarrell and

Sabey (1977) and cadmium by Garcia-Miragaya and Page (1976) and Street et al. (1977).

Bowman and Sans (1977), Van Bladel and Moreale (1977) and Yaron (1978) proposed the

use of Eq. 2.44 to describe the sorption of herbicides and pesticides on soils. Fitter and

Sutton (1975), Harter and Foster (1976) and White and Taylor (1977) fitted data on

phosphorous sorption on soil to Freundlich isotherm. Nathwani and Phillips (1977) reported

the equilibrium distribution of the hydrocarbons benzene, toluene, o-xylene and n-

hexadecane between the liquid and sorbed phase in soil following the Freundlich isotherm.

Note however that this sorption isotherm suffers from the same fundamental problem as the

linear isotherm, that is, there is no upper limit to the amount of the solute that can be sorbed,

so that the solid is never saturated.

Langmuir Sorption Isotherm

The Langmuir isotherm was developed by Langmuir (1918) based on the concept that

a solid surface processes a finite number of sorption sites. When all the sorption sites are

filled, the surface will no longer sorb the solute. The standard form of this isotherm is










p pm
C I + C (2.45)
k'2


where pm is the maximum amount of solute that can be sorbed and k'2 is a sorption constant

related to the binding energy.

The Langmuir model has been used extensively to describe the sorption of solutes,

i.e., metals, phosphorous etc., by soil. Thus, for example copper, lead, cadmium and zinc

sorbed to soil were shown to follow the Langmuir isotherm by Singh and Sekhon (1977a and

1977b), Harter (1979) and Shukla and Mittal (1979) in their studies on metals distribution

and transport by flow in soil. This isotherm was also used by Enfield and Bledsoe (1975)

and Novak et al. (1975) to model the movement of phosphorous in soils resulting from the

renovation of waste water by a land application treatment system.

All the equilibrium models assume that the rate of change of concentration due to

sorption is much greater than that due to the advective and diffusive transport. If this is not

the case, a kinetic model is needed.

2.5.2 Kinetic Sorption Models

Reversible Linear Kinetic Sorption Model

The most frequently used kinetic sorption model is the kinetic form of the linear

sorption isotherm, which is called a reversible linear kinetic sorption model,


P k'3C k',P (2.46)
dt








44

where k'3 and k'4 are forward and backward sorption rate coefficients. Equation 2.46 can

also be written in a different form (Nielsen et al. 1986)

k'4(KdC P) (2.47)
dt


where k'4 is the first-order rate coefficient. If sufficient time is available for the system to

reach equilibrium, dP/dt 0, so that P = KdC, which is the linear sorption isotherm.

One of the most frequent applications of Eqs. 2.46 or 2.47 is in the description of

sorption kinetics of phosphorous in soil. Among those who have used this model to describe

the movement of phosphorous through soil are Enfield and Bledsoe (1975), Enfield et al.

(1976), Shah et al. (1975) and Novak and Petschauer (1979). Leistra and Dekkers (1977)

applied this model to describe simultaneously fast and slow sorption phenomena that occur

with the addition of pesticides in solution to soil. Cho (1971) also used Eq. 2.47 for

calculations the convective transport of various oxides of Nitrogen in soil.

Reversible Nonlinear Kinetic Sorption Model

Corresponding to Freundlich sorption isotherm, the reversible nonlinear kinetic

sorption model is expressed as

dP = k'5C N k'6P (2.48)
dt


where k's and k'6 are the forward and backward sorption rate coefficients, respectively, and

N is a constant. When N = 1, Eq. 2.48 reduces to the reversible linear kinetic sorption

model. If the system reaches equilibrium, dP/dt -0, we obtain P = (k'5/k'6)C N, which

is the Freundlich sorption isotherm.








45

Homsby and Davidson (1973) used this model to describe the transport of the organic

pesticide fluometuron in soils. The distributions of the sorbed and solution phases of the

pesticide were well described at high flow rates. At low flow rates, where equilibrium

conditions existed, the kinetics of the sorption was not too important, and the process was

described equally well by the Freundlich isotherm. Enfield et al. (1977) and Fiskell et al.

(1979) found that phosphorous movement in the soil could be described with the reversible

nonlinear kinetic model with the value of N less than unity.

Bilinear Kinetic Sorption Model

The kinetic version of the Langmuir isotherm is given by the bilinear kinetic sorption

model:

d k' C (P m P) k'8P (2.49)
dt

where k'7 and k'8 are the constant. The theoretical foundation for Eq. 2.49 is the same as that

for the Langmuir sorption isotherm. If the time is sufficient, dP/dt 0, and Eq. 2.49 is

reduced to the Langmuir isotherm.

Gupta and Greenkorn (1973) and Kuo and Loste (1974) have applied the model to

the study of sorption of phosphorous on clay minerals. Despite its strong theoretical

foundation, Eq. 2.49 has not received widespread application. One reason is that the

constituent transport equation coupled with Eq. 2.49 is difficult to solve for.

Mass Transfer Model

If the rate of solute sorption is controlled by the mass transport process from solution

to solid surface, the mass transfer model is applied











dP k'8(C C*) (2.50)
dt


where k's is a sorption rate parameter that accounts for the diffusive transport of the solute

through a liquid layer surrounding the solid, and C* is the liquid phase concentration of the

solute in immediate contact with the solid surface. The mass transfer model has been used

by Navok and Pelschauer (1979) to describe orthophosphate sorption and used by Vilker

(1980) to describe the capacity of activated sludge to sorb pathogenic viruses.

All the isotherms and kinetic models discussed above are called one-box or one-step

models, in which sorption is a function of the solute concentration sorbed on the sorbent

(viewed as a completely mixed box) and concentration in solution (Lapidus and Amundson,

1952 and Oddson et al., 1970). However, some sorption processes are complicated, e.g.,

when a rapid initial intake is followed by a slower approach to equilibrium (Karickhoff,

1980), and for these cases the one-step model is not accurate enough to describe processes

kinetics. As a results, advanced model, which typically include more than one step, have

been applied.

2.5.3 Advanced Sorption Models

Diffusion-Sorption Model

To describe the sorption of hydrophobic organic chemicals, i.e., chlorobenzene

congeners, to and from suspended sediment and soil particles, Wu and Gschwend (1986)

combined diffusive penetration and the linear isotherm to develop their two-step sorption

model. The model is based on the following assumptions








47

(1) The ambient fluid is sufficiently turbulent that an exterior boundary layer does not limit

sorptive exchange.

(2) The porous sorbent, i.e., suspended sediment and soil particles, is spherical and

homogeneous. The rate at which the sorbate molecules diffuse through the pore fluids held

in the interstices of the porous sorbent is expressed as

9[(1-n)p,P'(r) + nC'(r)] = Dn 2C/(r) 2 C(r) (2.51)
at ar2 r ar



where C' is the solute concentration in the pore fluid, P' is the solid bound solute

concentration, n is the porosity of the sorbent, r is radial distance, p, is the specific gravity

of the sorbent, Dm is the molecular diffusion coefficient and (1-n) pP'(r) + nC'(r) is the local

total volumetric concentration in the sorbent.

(3) The solute concentrations in pore fluid and that bounded by solid are locally in

equilibrium and are described by linear isotherm

P' = KdC' (2.52)



By incorporating Eqs. 2.51 and 2.52 into the convective-diffusive transport equation, Wu and

Gschwend (1988) simulated the sorption of nonpolar organic chemicals transported in an

aqueous system containing a spectrum of particle sizes.

ME-SORB Model

For assessments of the impact of bottom sediment resuspension events on an aquatic

ecosystem, DePinto et al. (1994) developed the ME-SORB model. This model is intended








48

to be used in formulating a mechanistic description of metal ion sorption onto and/or

desorption from sediments. The following five steps are examined and included in the

model.

(1) Bulk transport--transfer of material from liquid bulk solution to the liquid surface film

surrounding the particle. In a well mixed suspension, this step is normally rapid and not rate

limiting.

(2) Film transport--transfer of the material through the surface film, which usually is a thin

layer of quiescent liquid lying between the bulk solution and the sorbent particle surface.

(3) Surface sorption--sorption of the material on to the surface of sorbent.

(4) Pore diffusion--transport of the sorbate radially between the particle surface and the

center of the particle through the intra-particle pore space.

(5) Pore sorption--sorption of diffused material on to the walls of the pores.

Each of these steps can occur in either the forward or reverse direction depending on

the sorbate gradient at a particular point. One or more steps may be insignificant compared

to others at a particular condition. The model was calibrated by resuspension experiments

carried in the Trenton Channel (Theis, 1988), and was applied to predict bulk solution

concentration versus time relations for lead, nickel and cobalt desorption from sediment

during a resuspension event.

Since the advanced sorption models include more transport and sorption processes,

they are usually more accurate in simulating the real process. However, the calibration

procedure for these models becomes more difficult and complicated than for simpler but less

accurate models. That is the reason why simpler sorption models are still widely used.











2.6 Sediment-Associated Contaminant Transport


The transport of contaminant in the three-layered water fluid mud bed system

shown in Fig. 2.7 must include dissolved contaminant transport, particle-bound contaminant

transport (related to sediment transport) and sediment-contaminant interaction, i.e.,

sorption/desorption. In this system, contaminant transport exhibits different characteristics

within each of the three layers. Contaminant fluxes across the water-fluid mud interface and

the fluid mud-bed interface represent the connective conditions for each of the two adjacent

layers and control the rates of contaminant exchange between them. The fluxes across the

water surface and bed bottom represent the boundary conditions.

2.6.1 Contaminant Transport in Water

In the water layer under wave motion, dissolved contaminant transport is governed

by the diffusion process, which includes molecular diffusion and wave-induced diffusion,

and also by sorption/desorption kinetics. Since particle-bound contaminant transport occurs

together with the sediment to which the contaminant is sorbed, the transport of particle-

bound contaminant is determined by sediment transport and the kinetics of sorption/

desorption. Sorption/desorption of contaminants onto/from the sediment is dependent on

contaminant (sorbate) characteristics, sediment sorbentt) characteristics and on water quality

(pH value, salinity, temperature, etc.).





























Figure 2.7 Sediment-associated contaminant transport processes.


Considering the water layer as a well mixed layer and ignoring the vertical transport

and distribution in water, Onishi (1982), O'Connor (1988a, 1988b and 1988c), Basmadjian

and Quan (1988) and Wang et al. (1991) used the depth-averaged contaminant concentration

of water layer in their transport models. Onishi (1982) formulated a horizontal two-

dimensional sediment and contaminant transport model named FETRA, by coupled a

sediment transport sub-model, a dissolved contaminant transport sub-model and a particulate

contaminant transport sub-model. The dissolved contaminant transport sub-model includes

(1) advection and diffusion/dispersion of dissolved contaminants; (2) sorption (uptake) of

dissolved contaminants by both moving and stationary sediment or desorption from sediment

into water; and (3) chemical and biological degradation, or radio nuclide decay of

contaminants. The particulate contaminant transport sub-model includes (1) advection and








51

diffusion/dispersion of particulate contaminants; (2) sorption (uptake) of dissolved

contaminants by sediments or desorption from sediments into water; (3) chemical and

biological degradation, or radio nuclide decay of contaminants; and (4) deposition of

particulate contaminants onto the river bed or erosion from the river bed. The sorption of

contaminant between the water and solid phases is described by the linear sorption isotherm.

The model was applied to the James River estuary to simulate the transport of sediment and

the pesticide Ketone.

O'Connor (1988a) has developed the equations that define the steady state

distribution of solids and sorptive chemicals in fresh water systems. The dissolved and

particulate phases of chemicals, as well as the sediment, are considered and yield a series of

six simultaneous equations for depth-averaged values in the water and bed layers considered

to be totally mixed. Instantaneous equilibrium is applied to the chemical sorption between

the dissolved and particulate states. The solution of the equations is applied to steady state

and time-variable conditions in (1) lakes and reservoirs (O'Connor, 1988b) and (2) streams

and rivers (O'Connor, 1988c) under different flow and wastewater discharge conditions.

Basmadjian and Quan (1988) developed the differential equations that describe the

fate of chemicals in rivers as they transfer, react and volatilize, both during contamination

and recovery. The sorption reaction in the water layer is given by linear isotherm. The water

column is assumed to be well-mixed and vertical and lateral concentration changes in the

water layer are neglected. Diffusive transport in the direction of flow is neglected compared

to advective transport in this direction. An explicit analytical solution is obtained for the 1-D

unsteady distribution of chemicals in both the aqueous and sediment phases.







52

Considering the vertical transport and distribution of contaminants in the water layer,

Hayter and Pakala (1989), Huber and Dickinson (1992), Sheng (1993) and Chen (1994) used

3-D models to simulate the contaminant transport in water column. The diffusion

coefficients of dissolved contaminants in water are same as the eddy diffusivity. The

particulate part of contaminants transports together with the sorbent, i.e. sediment, which can

be obtained by the coupled 3-D hydrodynamic and sediment transport models. The first-

order reversible kinetic model is used in these models to describe the sorption process.

Hayter and Pakala (1989) applied their CONTAM-3D model to a partially stratified tidal

river, Sampit River, South Carolina, to predict the lead transport and distribution in this river.

Huber and Dickinson (1988) used their water quality model for simulating various

phosphorus component distributions in Lake Okeechobee, Florida. Sheng (1993) and Chen

(1994) applied his model to Lake Okeechobee and Tampa Bay for prediction of phosphorus

and nitrogen transport transformation and distributions in both water and bottom sediments.

2.6.2 Contaminant Transport in Bottom Sediment

Compared to the movement in water, the movement of interstitial water in the bottom

layer tends to be considered slower. Thus, Onishi (1982) neglected contaminant transport

and sorption within the bottom layer. In his FETRA model only sorption/desorption between

water and bottom sediment surface is considered. However, since bottom sediment may be

an important sink and/or source of contaminants, contaminant transport and transformation

within the bottom layer must be taken into account. Contaminant transport in bottom

sediment includes dissolved contaminants transport, particulate contaminant transport and

sorption.







53

For modeling the vertical movements of pore water and dissolved constituents in the

bottom sediment layer, Berner (1980) gave the general diagenetic equation, which is

expressed as



ai z) a( Ci) + (2.53)
at az az


where Ci is the concentration of component i in terms of mass per unit volume of total

sediment (solids plus water), Di is the diffusion coefficient of component i, is the

velocity of flow relative to sediment-water interface, Ri is the rate of reaction and z is the

coordinate with origin at the sediment-water interface and directing vertical downward. The

first term on the right side of Eq. 2.53 is the diffusion term, the second term is the advection

term and the third one is the term for chemical, biological and radiogenic reactions. The

relative flow velocity and diffusion coefficient depend on bottom sediment characteristics,

overlying water motion and contaminant properties, etc. and are site-specific. To solve Eq.

2.53, \i, )i, as well as ai, must be provided.

For a mud bed, the self-weight consolidation is an important way by which advective

transport of water and its dissolved constituents is produced. A series of studies for one-

dimensional consolidation of saturated clays was carried out by Gibson et al. (1967, 1981),

Znidarcic et al. (1984) and Schiffman et al. (1984). Base on these studies, the general

consolidation equation in term of the void ratio, e, is expressed as:










P '1 d kw (e) ae a k,(e) do' ee e
1 [ 1+e] ae+ L a e) da/]e + ae = 0 (2.54)
p" de 1+e -z 9z pf(1 +e) de az at


where k, is the permeability which is a function of void ratio e, a' is the effective normal

stress and pf is the pore water density.

To solve Eq. 2.54 requires the effective stress/void ratio, o/(e), and the

permeability/void ratio, k,(e), relationships. By introducing the assumption that the

effective stress/void ratio and permeability/void ratio are relationships linear and that the

consolidation coefficient, CF = [-k(e)/pf(l +e)] do'/de, is a constant, Lee and Sills (1981)

solved Eq. 2.54 analytically. It should be noted, however, that the o/(e) andk(e)

relationships are in general nonlinear functions for real soils and are also site-specific.

Furthermore, the consolidation coefficient, CF, is usually not a constant. Thus, numerical

modeling is generally needed for solving Eq. 2.54. In that connection, Gibson et al. (1967

and 1981) have developed the theory and solutions for the finite nonlinear consolidation of

both thin and thick homogeneous layers. Macay et al. (1986) applied the theory to quiescent

consolidation of phosphatic waste clays. Since the o'(e) and k(e) relationships are site-

specific, experiments are required to supply these relationships for numerical modeling.

Znidarcic et al. (1984) has summarized existed testing procedures for laboratory

consolidation experiments and found that the current laboratory methods are restricted in

their applicability and only give approximate soil properties for theoretical calculation and

numerical modeling.










55

In the vicinity of the sediment-water interface, advective transport of pore water and

dissolved constituents is affected by the overlying water motion and thus is enhanced.

Savant et al. (1987) carried out laboratory experiments and numerical simulations to

investigate the transport of chemically inert, non-sorbed contaminants in a river sediment and

showed that interstitial fluid advection controlled contaminant transport within the stable

sediment bed with an in-bed Peclet number on the order of 100-1,000. These high Peclet

numbers indicated the negligible influence of molecular diffusion under the conditions

examined. Through an analytical solution of the two-dimensional Navier-Stokes equation

for oscillatory flow over a rippled bed, it was examined the transport of reactive solutes

(governed by a first-order kinetic model below the rippled bed) under wave motion and the

enhanced exchange of non-reactive solutes across the water-sediment interface. Shum

concluded that the wave-induced pore water circulation below the rippled bed and the total

wave-induced exchange across the water-sediment interface increased with the wave height

and decreased with the wave period.

For the mud bed, the permeability is much lower than that of sand bed, so that the bed

is typically considered to be impermeable over comparatively short time-scales, e.g., of the

order of wave motion. However, the mud bed may be fluidized under wave motion and form

a fluid mud layer. Thus, although advective transport may be negligible in the fluid mud

layer, the mixing process will be obviously enhanced because of its slurry-like properties and

oscillation under wave motion.

Contaminant diffusion in the interstitial water takes place in accordance with Fick's

laws of diffusion (Crank, 1975), which are










(1) first law:


Ji = -D-i (2.55)




(2) second law:



a. i a(Di z) (2.56)
at az az


where Ji is the diffusion flux of component i.

Within the undisturbed sediment that is relatively far below the sediment-water

interface and is not affected by the overlying water motion, diffusion can be only due to

molecular diffusion. Due to the presence of particles, it is not easy for dissolved

contaminants to diffuse in any direction within the sediment as they do in the overlying water

layer. Instead, diffusion is hindered by the solid particles and follows tortuous paths of fluid

flowing between and around particles. Mathematically, tortuosity, 0, is defined as (Fetter,

1981)

dl
0 (2.57)
dz

where dl is the length of the actual sinuous path over a depth interval dz. The diffusion

coefficient of component i in terms of tortuosity, is expressed as

Dm
Di = 0D (2.58)
02








57

where o9 is a coefficient that is related to the tortuosity (Bear, 1972). Perkins and Johnson

(1963) found that wo was equal to 0.7 in sand columns studies using a uniform sand. In

laboratory studies for geologic materials, Freeze and Cherry (1979) found that ao ranged

from 0.5 to 0.01. Also, according to Li and Gregory (1974) and McDuff and Ellis (1979),

an average 0 value for deep sea clays is 1.8. The molecular diffusion coefficients of some

ionic constituents in typical muds with porosity, n, are listed in table 2.1.

The typical molecular diffusion coefficient is seen to be in the range of 10"10 ~ 10'9

m2/s, while the kinematic viscosity, v, of water is around 10 Ih /s. Thus, the Schmidt

Number, Sc, which is the ratio of mass transfer rate to momentum transfer rate, i.e.,

Sc = v/D in the nonturbulent environment is about 1/1,000 1/10,000, an extremely low

range.

Table 2.1 Diffusion coefficients for some tracers in some typical marine mud beds.
Component Porosity, n Dm (10'1 m2/s)
Na 0.71 7.4

Ca+ 0.71 4.4
Cl- 0.71 10.2

SO4- 0.71 5.0

S04- 0.772 5.0

SO4- 0.64 4.0
NH4+ 0.72 9.8

HPO4- 0.72 3.6


Near the sediment-water interface, due to the effect of overlying water motion,

diffusion is not solely due to molecular diffusion. Vanderborght et al. (1977) analyzed the








58

vertical transport of dissolved constituents in a large muddy zone along the Belgian North

Sea coast. They selected a diffusion coefficient that was 100 times larger than that for

molecular diffusion down to 3.5 cm depth from the sediment-water interface. In the lower

compact layer diffusion was only due to molecular movement. This two-layered model of

bottom sediments was applied to simulate the vertical transport and profile of dissolved

silica, oxygen, sulfate, nitrate and ammonium.

DePinto (1994) in his Green Bay study classified the range of 0 ~ 4 cm depth below

bottom sediment surface as surface-mixed sediment layer, and the lower layer as subsurface-

mixed sediment layer. The fate and transport properties of contaminants in these two layers

were recognized and.modeled separately in his GBTOX model. Berger and Heath (1968)

used an "box-model" approach to represent the active surfacial sediment layer in which a fast

rate of mixing occurs over a certain depth over which sediment properties are uniform.

In the three-layered system shown in Fig. 2.6, the fluid mud oscillates under wave

motion. In this layer, contaminant diffusion will include the molecular diffusion and wave-

induced diffusion as a result of the effect from overlying water motion. Therefore, the

production, decay and transport of fluid mud can be expected greatly affect contaminant

transport between water and bottom sediment.

2.6.3 Fluxes Across the Sediment-Water Interface

Contaminant flux across the water-fluid or bed interface controls the rate of

contaminant mass transfer between water and bottom sediment. The accumulation of

contaminants in bottom sediments and the release of bottom contaminant are both controlled

by this flux. Generally, this flux is composed of dissolved and particulate contaminant








59

subfluxes. The dissolved part is transported by diffusion and advection, whereas the

particulate part is transported together with the sorbent, i.e., sediment. Thus, resuspension

and deposition of sediment can strongly influence the particulate contaminant flux across the

interface.

The transport of materials across a solid boundary surface and a moving fluid or a

interface between two relatively immiscible moving fluids is defined as convection (Welty,

et al., 1969). The flux of convective mass transfer is expressed in the form

Fi = k ACi (2.59)



where F, is the mass flux of component i across the interface, ACi is the concentration

difference of constituent i across the interface and kc is the convective mass-transfer

coefficient.

The so called film theory for mass transfer is based on the assumption of the presence

of a fictitious film at the interface that offer the same resistance to mass transfer as actually

exists in the entire field. Accordingly, the convective mass transfer coefficient is modeled

as

D.
kc =- (2.60)
8f



where Di is the molecular diffusion coefficient of component i and 86 is the film thickness.

Thus, the mass transfer coefficient, ke, is a function of molecular diffusion coefficient Dm and

the chemical and hydrodynamic parameters that determine the film thickness, namely, water







60

viscosity, v, bottom friction velocity, u,, and the Schmidt number, Sc (Boudreau and

Guinasso, 1982). Expressions for kc are generally expressed as

kc = l2c u,Sc P 12 (2.61)


where coefficient a12c is in the range of 0.04 1.0 and P12c is in the range of 2/3 1.

The so-called penetration theory was first proposed by Higbie (1935) based on the

idea that the diffusive component only penetrates a short distance into the phase of interest.

This theory has been subsequently applied to turbulent flow by Danckwerts (1951). The

convective mass-transfer coefficient based on this theory is expressed as

kc = (2.62)



where s is the surface-renewal factor. Toor and Marchello (1958) have pointed out that the

penetration concept is valid only when surface renewal is relatively rapid, in which case

kc ~ For relatively slow surface renewal, the film theory is valid in which kc ~ Di.

In reality the convective mass-transfer coefficient is proportional to a power of the molecular

mass diffusivity, Di, between 0.5 and 1.0.

In studying diffusive fluxes across the sediment interface, Morse (1974) considered

that there exists a stagnant benthic boundary layer just over the sediment-water interface.

The transport of dissolved constituents across this layer is purely by molecular diffusion,

while the transport in the main water column overlying the boundary layer is by turbulent

mixing. The maximum possible thickness of the stagnant layer is on the order of 1 cm,

which is within the limit of the calculations of Wimbush (1970) for the South Pacific.







61

Santschi et al. (1983) investigated the resistance of chemical transport within the deep-sea

boundary layer and concluded that the equivalent stagnant boundary film thickness is about

0.47 mm. The result is based on the directly measurements of CaCO3 dissolution and Mn"

released from bottom sediment at a site in the eastern Pacific.

Under wave motion the exchange of water and dissolved constituents between water

and bottom sediments is evidently enhanced due to wave-induced diffusion and advection

in the near interface layer. Savant et al. (1987) and Shum (1992,1993) examined

contaminant release from sandy beds under wave motion. They found that wave-induced

advection, which causes a flux across the interface, is so great that molecular diffusion can

be neglected.

In contaminant transport modeling, DePinto (1994) used a diffusion process which

included the effects of diffusion and advection induced by external hydrodynamics to

describe contaminant transport across the sediment-water interface. Hayter and Pakala

(1989) considered contaminant sorption/desorption onto/from the bottom sediment surface

and advection due to bottom sediment consolidation in their CONTAM-3D model. Chen

(1994) only included advective transport due to the hydrodynamic effect on the bottom but

neglected the effect of diffusion in his three-dimensional contaminant transport model.

Particle-bound contaminant flux has been shown to be related to the sediment

entrainment and deposition rates and to contaminant sorptive properties in water and fluid

mud or bed (Onishi, 1981; O'Connor, 1988; Hayter and Pakala, 1989, DePinto, 1994 and

Chen, 1994). However, one issue that has not always been fully accounted for by most

investigators is that together with the entrainment and deposition of sediment, water is also







62

entrained and deposited. Thus, sediment mass transfer between the water and fluid mud or

bed layers can not only induce particle-bound contaminant transfer between the two layers,

but also enhance dissolved contaminant transfer. This is the dissolved contaminant mass

transfer through water exchange induced by sediment entrainment and deposition, which

must be considered when entrainment and/or deposition take place.

2.6.4 Fluxes Across the Fluid Mud-Bed Interface

Contaminant transfer across the fluid mud -bed interface can also be divided into two

parts: dissolved part and particulate part. When the bed is fluidized or fluid mud dewaters

to become part of bed, the particle-bound contaminants will be effectively transported across

the interface. However, under those situations in which only an equilibrium fluidization

depth occurs, as in the present case, there will be no sediment mass transfer is considered

across the interface and also no particulate contaminant transport across the interface.

For dissolved contaminants, since around the fluid mud-bed interface there is

typically no disturbance from the overlying water motion, molecular diffusion may be the

only diffusion process across the interface. In the GBTOX model (DePinto, 1994), the

transfer of unbounded PCB between the surface-mixed and the subsurface-mixed sediment

layers is only by molecular diffusion. Vanderborght et al. (1977) also considered only the

molecular diffusion to describe dissolved silica flux across the interface between the top 3.5

cm bed layer and the more compact lower layer of the bed.

Consolidation may be the main advective process for dissolved contaminants across

the fluid mud-bed interface. However, typically consolidation is a slow process, in








63

comparison with wave-induced transport. Thus, for example for an episodic event,

consolidation is usually neglected.













CHAPTER 3
MUD FLUIDIZATION BY WAVES


3.1 Introduction


The theological and mass transport characteristics of fluid mud can be significantly

different from those of the non-fluidized bed. Thus, once fluid mud develops, it must be

considered separately from the non-fluidized bed, as noted in Section 2.3.

The main step for setting up the three-layered water-fluid mud-bed system is the

determination of the thickness of the fluid mud layer. Fluidization is a time-dependent

process starting with a bed over which wave motion commences initially in clear water.

Thus, it is a function of the wave characteristics and bottom mud properties. In this chapter,

by assuming the mud bed to be a single-phase continuum, fluidization is considered in terms

of forcing due to cyclic normal pressure loading and the horizontal pressure gradient. First,

the mechanism of fluidization of mud beds by waves is examined. The bed is considered to

fluidize when the effective submerged weight of the particle or floc is exceeded by the

upward inertia force due to bed vibration. Then, by characterizing the bed as a uniaxial

extensional-Voigt solid, it is represented in terms of an equivalent spring-dashpot-mass

system. The dependence of the fluidization depth on characteristic wave and bed theological

parameters is examined for a water-bed and a water-fluid mud-bed system represented,

respectively, as one-degree and two-degrees of freedom analogs. Theoretical results obtained







65

are compared wave flume data obtained by Ross (1988), Lindenberg et al. (1989) and Feng

(1992) on fluid mud thickness. Finally the model is applied to lake Okeechobee in Florida,

where fluid mud thicknesses were measured previously.


3.2 Mechanics of Fluidization


3.2.1 Vertical and Horizontal Motions of Bed under Waves

For a mud bed under waves, two aspects of wave motion can be distinguished (Ross,

1988): "pumping" due to cyclic normal stress on bed surface and "shaking"due to cyclic

shear stress on bed surface. Pumping is responsible for bed motion in the vertical direction,

while shaking may cause bed motion in the horizontal direction.

The gradients of pressure and shear stress on the bed provide the forcing for the

horizontal motion of the bed. Dalrymple and Liu (1978) compared results on water wave

attenuation from their wave-soft bed interaction model with results from Gade's (1957)

inviscid, shallow water model, and found that despite Gade's neglect of viscosity in the upper

fluid, and therefore absence of shear stress at the interface, both solutions agreed reasonably

well with the laboratory data collected by Gade. A conclusion can therefore be drawn that

the principal mode of energy transfer to the mud is the normal stress rather than the shear

stress, due to wave-induced work on the lower medium. Isobe et al. (1992) carried out

experiments to check the predominance of forces for mud bed horizontal motion. In one

experiment, the bed was covered with a nylon sheet which transferred the pressure and but

not the shear stress. A second experiment was done without cover. The results showed that

wave height decay with and without the cover were almost same over a wide range of








66

incident wave heights. This also implies that the pressure gradient due to wave motion is the

dominant external force for the mud horizontal motion and wave energy dissipation.

Under wave motion mud beds are known to fluidize, and a fluid mud layer of

equilibrium thickness is observed to occur after a certain elapsed time depending on the

initial conditions with respect to the mud-water system and the forcing wave characteristics.

Thus, a mechanistic framework for explaining mud bed fluidization must be based on a

consideration of forces required to cause particle-particle separation, hence a loss of effective

stress. These forces can be considered in three ways: (1) forces in the vertical direction, (2)

forces in the horizontal direction and (3) combination of vertical and horizontal forces.

3.2.2 Bed Failure by Horizontal Forces

Madsen (1974) hypothesized that a large horizontal pressure gradient can cause bed

failure. The criterion for failure was expressed in a non-dimensional form:


SP tanpw (3.1)
Pwg ax crit Pw



where p, is the wave-induced pore pressure in excess of the hydrostatic pressure, p is the

water density, g is the gravitational acceleration, p3 is the bed density and ( is the friction

angle. This shear failure criterion is applicable only to non-cohesive sediment, because the

effects of cohesion and rheology are not included. Modifying Eq. 3.1 by introducing

cohesion, Ch, and the multiplying factor pgD for both sides of the equation, we obtain a

more general, stress-form, criterion










( D= pwg'D tan +Ch (3.2)




where the effective gravitational acceleration, g = g(p3 Pw)/Pw and D is the diameter of

the particle or floc. By using the definition of the effective stress a' = pg'D and referring

to the well-known Coulomb equation for shear strength, Ts = o/tan) + Ch, Eq. 3.2 can be

expressed as


D = pg /D tan + Ch
ax crit (3.3)

= a/tanO + C =



Thus, when the horizontal pressure difference equals the bed shear strength, the mud bed

fails. The inter-connections between the particles or flocs are cut off at that level where

Eq.3.3 is satisfied and the bed above that level is fluidized at that instant.

Although Madsen (1974) successfully used the criterion, -(ap /x)crit/pwg = 0.5,

for loose sand liquefaction, the use of Eq. 3.3 for the mud bed may lead to an

underestimation of fluidization. The reason is that Eqs. 3.1, 3.2 and 3.3 are obtained by

considering forces in the horizontal direction only. For sandy beds this may be acceptable

because there may be practically no vertical motion of the bed under waves. However, for

the mud bed, oscillations under wave action are typically significant and cannot be neglected.

In the following development, we show that a vertical oscillation of the mud bed

produces an upward inertia stress, oi, that can greatly reduce the effective stress. Also, the







68

buildup of the excessive pore pressure, Au,, will reduce the effective stress. Thus, Eq. 3.2

can be applied for the mud bed under long wave action, in which motion in the vertical

direction is negligible and the excessive pore pressure buildup is minor.



FF
SFluidized Layer

F jf2g
f4 mpg' F2 p


Bed In vertical direction
(a) (b) (c)

Figure 3.1 Forces on a particle or floc. F,, F2, F3 and F4 = normal forces from adjacent
particles; f,, f2, f3 and f 4 = shear forces from adjacent particles; Li = inertia force; L
cohesive resistance; mp = particle mass and g' = effective gravity: a) Bed and fluidized mud
with tagged particle forming a part of the lower boundary of fluid mud; b) forces on tagged
particle; c) forces in the vertical direction.



3.2.3 Bed Fluidization by Vertical Forces

Consider a particle (or a cohesive floe treated as an integral particle) mass mp in the

mud bed under wave motion as shown in Fig. 3.1. Four types of forces acting on this particle

must be recognized: (1) effective gravity or buoyancy in water, (2) inter-particle cohesive

forces, (3) normal and shear forces due to contacts between adjacent particles, and (4) inertia

force due to vibration, L,(t), under wave loading. Considering the forces in the vertical

direction, the normal and shear forces (F1, F2, F3, F4, fl, f2, f3, and f4) due to contacts

between adjacent, almost randomly positioned, particles can be represented together as a




University of Florida Home Page
© 2004 - 2010 University of Florida George A. Smathers Libraries.
All rights reserved.

Acceptable Use, Copyright, and Disclaimer Statement
Last updated October 10, 2010 - - mvs