Group Title: 7th International Conference on Multiphase Flow - ICMF 2010 Proceedings
Title: 17.3.2 - Liquid effects on the velocity profile of granular flows in a rotating drum and flow categorization
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Title: 17.3.2 - Liquid effects on the velocity profile of granular flows in a rotating drum and flow categorization Granular Media
Series Title: 7th International Conference on Multiphase Flow - ICMF 2010 Proceedings
Physical Description: Conference Papers
Creator: Yang, F.-L.
Huang, L.-H.
Publisher: International Conference on Multiphase Flow (ICMF)
Publication Date: June 4, 2010
 Subjects
Subject: granular flow
solid-liquid two-phase flow
rotating drum
PTV
flow classification
 Notes
Abstract: This paper describes an image analysis routine to investigate solid-liquid granular flows in a thin rotating drum. New findings of liquid effects on modifying the granulate dynamics are reported. The major contribution of this work, nonetheless, is to propose a flow classification criterion for liquid-included granular flows by comparing the averaged surface velocity, Us, with respect to the drum speed, ω. This criterion is based on a model proposed earlier by Tegez et. al (2003) exclusively for the motion of wetted granular mixtures that employed only particles with damp surfaces. Experimental results for submerged, immersed, wetted, and dry bulks are integrated here to generate a Us-ω plot on which a granular, a transition, or a viscoplastic bulk flow may be categorized.
General Note: The International Conference on Multiphase Flow (ICMF) first was held in Tsukuba, Japan in 1991 and the second ICMF took place in Kyoto, Japan in 1995. During this conference, it was decided to establish an International Governing Board which oversees the major aspects of the conference and makes decisions about future conference locations. Due to the great importance of the field, it was furthermore decided to hold the conference every three years successively in Asia including Australia, Europe including Africa, Russia and the Near East and America. Hence, ICMF 1998 was held in Lyon, France, ICMF 2001 in New Orleans, USA, ICMF 2004 in Yokohama, Japan, and ICMF 2007 in Leipzig, Germany. ICMF-2010 is devoted to all aspects of Multiphase Flow. Researchers from all over the world gathered in order to introduce their recent advances in the field and thereby promote the exchange of new ideas, results and techniques. The conference is a key event in Multiphase Flow and supports the advancement of science in this very important field. The major research topics relevant for the conference are as follows: Bio-Fluid Dynamics; Boiling; Bubbly Flows; Cavitation; Colloidal and Suspension Dynamics; Collision, Agglomeration and Breakup; Computational Techniques for Multiphase Flows; Droplet Flows; Environmental and Geophysical Flows; Experimental Methods for Multiphase Flows; Fluidized and Circulating Fluidized Beds; Fluid Structure Interactions; Granular Media; Industrial Applications; Instabilities; Interfacial Flows; Micro and Nano-Scale Multiphase Flows; Microgravity in Two-Phase Flow; Multiphase Flows with Heat and Mass Transfer; Non-Newtonian Multiphase Flows; Particle-Laden Flows; Particle, Bubble and Drop Dynamics; Reactive Multiphase Flows
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7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30-June 4, 2010


Liquid effects on the velocity profile of granular flows in a rotating drum and flow
categorization


Fu-Ling Yang and Li-Hsiang Huang

National Taiwan University, Assistant Professor, Mechanical Engineering
No.1, Sec.4, Roosevelt Rd., Taipei, 106, Taiwan
fulingyang@ntu.edu.tw


Keywords: granular flow, solid-liquid two-phase flow, rotating drum, PTV, flow classification

Abstract

This paper describes an image analysis routine to investigate solid-liquid granular flows in a thin rotating drum. New findings
of liquid effects on modifying the granulate dynamics are reported. The major contribution of this work, nonetheless, is to
propose a flow classification criterion for liquid-included granular flows by comparing the averaged surface velocity, U,, with
respect to the drum speed, o. This criterion is based on a model proposed earlier by Tegez et. al (2003) exclusively for the
motion of wetted granular mixtures that employed only particles with damp surfaces. Experimental results for submerged,
immersed, wetted, and dry bulks are integrated here to generate a U,-o plot on which a granular, a transition, or a viscoplastic
bulk flow may be categorized.


Introduction


The dynamics of dry granular matter has formed an active
research field for more than two decades for its prevalence
in both natural and industrial processes. Unlike typical
single-phase materials, a granulate assembly can exhibit
fluid-like and solid-like behaviors simultaneously under
external loading, possessing a transition zone within the
bulk. This peculiar behavior has attracted many researchers'
attention with the hope to develop a feasible dynamic model.
Nonetheless, the dual-nature of the mixture properties posts
great challenge on theoretical analysis and lab-scale
experiments have become a popular research means to
investigate the mixture dynamics. A rotating drum has been
a popular facility to generate continuous surface flow and
the resulting dry bulk dynamics is commonly investigated
with respect to the flow Froude number Fr =R20/g-with R,
o, and g denoting the drum radius, angular velocity, and
gravity (Jain, Ottino, & Lueptow 2004)-into avalanching,
rolling or cascading, cataracting, and centrifuging regimes.
Here, we chose the drum speeds (below 6rpm) to ensure a
rolling phase that ensures a nearly flat bulk surface profile.
The most well-know feature of such surface flow is the
linear velocity-depth profile remained over a few particle
diameters near the free surface which transits into an
exponentially decaying profile with flow depth (Courrech
du Pont et. al 2005, Forterre and Pouliquen 2008, GDR
Midi 2004, Jain, Ottino, and Lueptow 2004, Orpe and
Khakhar 2007).
While the dynamics of dry granular mixtures have been
widely explored, our knowledge of how the presence of
liquid may affect the collective motion of granulates is
fragmental and rather limited. There exist a few pioneering
experimental works that consider two limiting cases of
solid-plus-liquid mixtures. The first class considers particles


with damp surfaces and the deviation between any bulk
dynamics from that exhibited by a dry bulk is examined by
considering the cohesion force developed in the interstitial
liquid films. This type of mixtures will be referred to as a
wetted bulk in this work. Tegzes, Vicsek, and Schiffer
(2003) measured the surface velocity, U,, of a wet bulk with
respect to the drum speed, o, and categorized the bulk into
a typical granular flow or a viscoplastic flow according to
the U,-o correlation. For a granular flow, they found U,=
Ao2/3, which confirms the theoretical prediction by Arrason
and Tsimring (2002). In the viscoplastic regime, U = Bo
was observed and U, is slower than the dry value by a factor
around 2. These authors also measured the bulk velocity
along the drum centerline and slightly concave velocity
depth profile was discovered mimicking the motion of
liquid. More surprisingly, these authors reported the
formation of a thin plug layer near the free surface within
which the particles stayed rest to each other and experience
zero strain. Brewster, Grest, and Levine (2009) reproduced
the surface plug flow in the discrete-element simulation by
introducing a cohesion force in to the conventional contact
model. They explained that the plug was formed since the
weight of the overlying material could not overcome the
finite yield stress induced by the interstitial liquid cohesion.
Thus, a bigger plug was produced when the cohesion
strength was increased.
The second class of study fully fills the drum space with
excessive liquid creating a pure solid-liquid two-phase flow,
which will be termed as a submerged bulk. Jain, Ottino, and
Lueptow (21i '4) measured the bulk velocity depth profile at
the midstream and found a slower bulk motion than the dry
case at the same co. If scaled by U, and the flowing layer
thickness 6, the measured velocity depth profiles were
found dynamically similar to each other which led the
authors conclude that the bulk dynamics is not strongly
altered by the coexisting liquid. However, if we examined









the reported Us with respect to o0, it is very interesting to
discover that all the investigated flows obey the condition
that U,> Ao2/3. This particular finding led us to speculate let
us speculate whether the categorization proposed by Tegzes
et. al (2003) for wetted bulks-namely the U= Ao)2 or Bow
correlation-also applies to other types of solid-liquid
granular flows.
The main purpose of this work is thus to answer this
speculation with systematic experiments. To extend the flow
conditions, we prepared a third type of solid-liquid mixtures
where the particles are fully immersed in the liquid but the
drum space is left unfilled. An interface is thus created
which boundary condition may modify the bulk motion
leading to new bulk dynamics. In addition to bulk surface
velocity, we also examine the depth profiles of bulk velocity
and the shear strain rate with respect to the flow
classification. The flowing thickness, 6, is also monitored
which quantity is typically defined at the interface that
separates the moving assembly from the rest bulk in
solid-body rotation with the drum. To achieve this, an image
analysis routine has been developed to monitor individual
particle motion using PTV (particle-tracking velocimetry).
The individual particle motion is then averaged to estimate
the mixture motion, as a continuum, by an area-weighted
mean.


Nomenclature


A,B fitting coefficients
D sphere diameter (mm)
Fr = R2m/g flow Froude number
g gravitational constant (ms-2)
Ni position of neighboring spheres (pixel)
Pi position of sphere locator (pixel)
R drum radius (cm)
UB bulk velocity at grid (cms 1)
Uc bulk characteristic velocity (cms 1)
U bulk velocity after x-average (cms 1)
U = U / Uc, normalized bulk velocity
W drum width (cm)
t time (second)
x, grid position (pixel)
X,Y coordinate in the drum fixed coordinate (cm)
Y =Y/R, normalized flow depth


Greek letters
/3 particle trajectory angle (radians)
free surface inclination angle (radians)
6 flowing layer thickness (cm)
pp,,f solid, liquid density (gcm-3)
,f liquid viscosity (cP)
m drum speed (radians s-')


Subsripts
max maximum
I,J Index


7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30-June 4, 2010

Experimental Facility and Flow Condition


As sketched in Figure 1, a thin rotating drum of an inner
radius R=17.5 cm and width W=6 cm has been constructed
with plexiglass. The drum was half-filled with granular
mixtures composed of mono-disperse POM spheres
(diameter D=4.76 mm and density p, =1.4 g/cm3) of
identical total weight, with or without the interstitial liquid.
The drum was driven at a range of angular velocities, from
o = 0.73 to 6rpm, chosen carefully to ensure that a nearly
flat surface was formed at flow steady states. For the dry
bulk, the flow Froude number falls in the range of
Fr=3x10-4 to 8.26x10-3, entirely in the rolling regime. Three
Newtonian liquids, water and two water-glycerol mixtures,
were used and their density and viscosity at room
temperature (-25 C) are pf=0.997, 1.232, and 1.236 g/cm3
and pf=0.893, 150, and 200 cP, respectively. The resulting
mixture is described as wet, immersed, or submerged
according to the amount of liquids. The liquid type will also
be specified with descriptions like 'water-wetted' or '150 cP
glycerol- submerged'.
The bulk motion was monitored from the drum lateral side
by a high-speed digital camera at 500 frames per second
(fps). This shooting rate was chosen to meet the particle
displacement condition required in our PTV algorithm. The
whole flow domain was monitored at a resolution of
1280-by-1024 pixels, after rotating the camera frame in line
with the free surface, and each sphere diameter spanned at
least 17 pixels in the images. Since the drum width was
filled by only 11 to 12 spheres, the resulting bulk motion
was assumed to be nearly two dimensional. The motion of
the spheres lied adjacent to the drum lateral wall should
suffice to represent the bulk motion across the drum width
and thus should effectively reveal the liquid effects on the
bulk motion. The addition of liquid may cause the spheres to
stick to the side wall under certain flow conditions. The
frequent contacts with other spheres away from the wall,
however, help to disturb and counteract the possible liquid
force developed between the wall and the near-wall spheres.
Thus, the motion of wall on altering the sphere motion is
expected to be secondary. Some wet spheres that remained
attached to the wall obscured the measurements of upstream
surface profile. Thus, the surface slope was estimated
statistically using the measured particle motion near the free
surface, which procedure will be introduced later.


Illumination





Camera 500 fps


Figure 1: Sketch of the rotating drum facility









Particle-Tracking velocimetry and Post Analysis


Fig. 2 (a) shows a portion of a grayscale raw image captured
in the experiments. The bright spots formed on the POM
surface due to the light source were employed to locate the
individual spheres. The light source induced high-frequency
noises were first filtered by a Gaussian filter. A Laplacian
filter was then applied to enhance the image contrast,
transforming bright spots into separate white patches in Fig.
2(b). The characteristic length scale of these patches was
estimated to be around 1/4D. Within each patch, a search
routine was performed to locate every pixel that possessed
an intensity value above a threshold. The locations of these
identified pixels were averaged to obtain a mean position, P,
(x) xt = (x, y,), as a sphere locater at time t.
Most of the unwanted bright spots on the second-layer
spheres can be filtered out by choosing an appropriate
intensity threshold, estimated by the image histogram. A
check routine was still applied to fully remove the
second-layer locators. We first calculated the distance
between each P, (x,) and its three most adjacent neighbor
locators, N,1 (x,) N,3(,3t), as dk- _/, -_I with k=1-3.
If the mean of d,1, d,2, and d,3 falls below 0.9D, P, (x,, y) was
eliminated. To initiate this final check routine, a sphere had
to be manually selected from the first-layered spheres. The
obtained sphere locators were imposed onto the original
image and the result is shown in Fig. 2(c).


7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30-June 4, 2010

circle, the sphere locator of particle A2 that possessed the
shortest distance to P, (x,) at time t+At was determined to
be the same sphere monitored at time t. The instantaneous
displacement vector, iA. I was then divided by the elapsed
time At to calculate the instantaneous velocity vector for the
sphere A1. This matching routine continues until all the
spheres are paired between two images. The success of such
a simple tracking algorithm crucially relies on a sufficiently
small displacement vectors. Such a precondition was met by
choosing a camera shooting frame rate high enough to
ensure that no sphere travelled more than 1/4D the length
scale of the bright patches in Fig.3(b)- between two
consecutive snapshots. The current 500 fps frame rate was
determined by trial and error. Of course, the sufficient image
resolution also helped to facilitate this track routine.






+
+^ + ^7\/ Yr






the nearest neighbor.


(b)





-Ar
tL~rr-~E~~~~r4.~


Figure 2: Image processing routine: (a) the raw grayscale
image (b) the image after the Gaussian and the Laplacian
fitering (c) the obtained sphere locators.

Particle tracking was achieved by the method of the nearest
neighbor (BOhm et. al 2006). In Fig. 3(a), let P, (x,) denote
the position of the locator of sphere A in the image taken at
time t. A search circle of radius D was located precisely at
P, (x,) on a subsequent image at time t+At, as portrayed by
the large dotted-dashed circle in Fig. 3(b). Within this search


Figure 4: A drum-fixed coordinate system adopted here.

To present the bulk motion, an orthogonal coordinate
system was defined on the nearly flat free surface with the
positive X-axis pointing downstream and the Y-axis
pointing away from the mixture (see Fig. 4). Such a
coordinate system was inclined from the actual horizontal
by an angle /, whose value varied with the drum speed and
the mixture composition. To determine / in a consistent
manner, a statistical approach was developed as describe
below. A screening window was first selected manually
beneath the free surface near the drum center as the dashed
box in Fig. 4. All the sphere displacement vectors that fell in
this screening box were monitored for 50 consecutive
frames. The slope of each displacement vector was
converted to an inclination angles /, to the first digit. The
occurrence of each angle, N(3,), was counted found to peak









between 20 and 40 for all the examined mixture motions.
The result obtained for the water-immersed bulks, chosen as
an example, is shown in Fig. 5(a). The top 30 probable
angles measured in each bulk motion were averaged to
estimate / and the coordinate system was rotated
accordingly.


Im -20 20 m i
p (deg)


Figure 5: (a) Counts of the inclination angle of individual
sphere trajectories in a_water-wetted mixture, where a mean
value was estimated / =20.41.56; (b) Illustration of area
weighting schme for the calculation of UB(xy).

To describe the mixture as a continuum, a spatial average
was performed using an averaging square B with a side
length of 2D. This averaging box was staggered over the
bulk with a constant shift 0.5D in the X- and Y-directions, as
that depicted in the bottom of Fig. 4. The box geometric
center, B(x,y), generates a grid of uniform spacing 0.5D
across the bulk. At a specific time k, the mixture average
velocity vector at a location (x,y) was calculated by the
motions of the N spheres that fell entirely or partially in
B(x,y) as

LB (Xy)k = (E l "JlJ/Z Nlaj)

where u) and a denote the instantaneous velocity vector of
each sphere and its partial area that overlaps with B(x,y) as
those shaded in Fig. 5. The resulting mixture averaged
velocity distribution has a spatial resolution as high as 0.5D,
which suffices to capture any sharp variation in the bulk
dynamics. After a time sequence of UB(x,y)k was computed, a
temporal average was performed to estimate the mixture
quasi-steady profile, UB(x,y), by averaging five sets of ten
consecutive data, with a constant 0.2 second time span
between each set. Note that the calculations of UB(x,y)
employ the sphere projection area, instead of its actual
volume, to present the sphere occupation. Thus, these
formulas may overestimate the actual three-dimensional
values. However, considering the quasi-2D nature of the
mixture averaged flow, the obtained results should suffice to
characterize the mixture behaviors.
To emphasize variations with the flow depth, a secondary
spatial average along the X-axis was performed to smooth
out streamwise data fluctuations at the particle size level. A
probing stripe of width 8D was located at x,=0 and the
mixture averaged velocity at a specific flow depth y, was
calculated by the arithmetic mean of UB(x,y) with x,-4D < x
< x,+4D. The obtained bulk properties are denoted by U(Y)
without the subscript B and the 0.5D spatial resolution is
preserved along the flow depth.


7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30-June 4, 2010

Results and Discussion
Fig.6 shows the depth profiles of U(Y*), with Y*=Y/R,
measured along the drum centre line in each mixture motion
driven at o0=3.94 rpm. As portrayed by the open-circle-solid
line (0), the dry bulk exhibited a linear velocity-depth
profile near Y =0 which is a well-known phenomenon for a
collision-rich dry surface flow. A surface velocity of about
35 cm/s was measured which surpassed the surface motions
of all the rest liquid-included mixtures. The deduction of
surface velocity, Us, with the presence of interstitial liquid
may be attributed to viscous dissipation when surface
spheres collided during their downstream motion. It is
interesting to find that the second fast surface motion was
developed in the water-submerged mixture that showed
analogous U(Y*) profile-almost linear-near the free
surface, plotted by the open-square (0) line. Only slight
deviation was observed as Y*- 0. Other liquid-included
mixtures exhibited much slower surface motions and
distinct depth profiles. For example, as shown by the
open-triangle-solid line (A), the water-wetted mixture
exhibited a concave velocity profile similar to that measured
by Tegzes et. al (2003) suggesting the formation of a very
thin plug layer.
When these spheres were fully immersed in the liquid, the
buoyancy force helped mobilize the particle assembly,
resulting in a thicker layer of downstream moving spheres.
The liquid may even accumulate sufficient inertia to
interfere with the sphere motion, resulting in dramatic
changes of previously examined U(Y*) to more blunt
profiles at smaller magnitudes as observed in the motions of
the water-immersed and the two glycerol-immersed
mixtures as portrayed by the open-diamond (0), the
solid-circle (0), and the solid-square (0) lines, respectively.
It is very interesting to observe a diminishing depth gradient,
[U/OY near the free surface of these mixtures suggesting a
liquid-like behavior. Such a liquid-like bulk behavior was
also observed on the glycerol-wetted mixture motion,
depicted by the solid-triangle line (A), possibly due to the
strong cohesion force. Deviations in the bulk streamwise
velocity depth profiles serve as preliminary evidences of
liquid dissipation of particle kinetic energy and its
modification of bulk momentum transport mechanism.
While dissipation increases with pf, interstitial liquid of
greater pf can provide larger buoyancy mobilizing the
mixture and enhancing the mixture momentum transport.









Figure 6: Velocity depth profiles in the drum centre (see the
shaded zone) using various mixtures and w= 3.94 rpm.

All the investigated mixtures went through non-linear
deceleration as going deeper into the bulk. Each profile
eventually merged onto a linear segment of negative U(Y*)
which moved with the drum motion as an incompressible
continuum medium in solid-body rotation. The dry, the
water-wetted, water-immersed, water-submerged, and the
150cP glycerol-wetted mixtures seemed to collapse onto a
common profile. However, the lower bulks of the two
glycerol-immersed mixtures exhibited distinctive off-sets
from that common linear profile, suggesting the formation
of a lubrication liquid layer near the drum wall. This may be
confirmed when the bulk wall velocity, U,a11, was compared
to the drum circumferential velocity, Udrum =R=7.33 cm/s.
Only these two glycerol-immersed mixtures possessed Uaii
below Udrum at a degree increasing with pi and pf. Both the
lubrication force and the buoyancy force in the immersed
mixtures can provide normal support to the particle
assembly that effectively diminished the wall friction and
thus led to a greater wall slip.
According to the bulk velocity depth profiles, these mixture
motions may be categorized into three distinctive groups: (1)
a faster group possessing linear sections near Y=0 (the dry
and the water-submerged mixtures: O and 0), (2) a slower
class showing blunt concave profiles across the flowing
mixture with nearly zero surface gradient (the two
glycerol-immersed and the glycerol-wetted mixtures:*,E,
and A), and (3) the rest profiles they possessed concave
profiles near the surface but moved at a noticeably greater
velocity (the water-wetted and the water-immersed mixtures:
A and 0). It is thus wondered if the two U,-o correlations
proposed to categorize wetted bulk flows have any relation
to these three types of velocity profiles. In other words, it is
of particular interest to examine if the type-1 bulk motion
obeys U, > Ao2/3 to suggest a granular flow type mixture
motion despite the presence of interstitial liquid. Similarly, it
is interesting to examine if a type-2 mixture possesses a
surface velocity that U, < Bo and flows like a viscoplastic
liquid medium. Type-3 mixtures motion will then be termed
as in the transition phase that flowed with sufficient inertia
in the solid phase but possessed a diminishing strain rate
near the free surface-suggesting a localized liquid-like
behaviour.
The solid-liquid mixtures were driven to their steady states
using a wider range of drum speeds, from 0= 0.78 to 6 rpm.
For each mixture, the measured surface velocity, after
spatial and temporal average, are plotted as a function of
drum speed in Fig. 7. The coefficients A=20.785 and
B=33.588 for the two U,-o correlations were fitted from the
experimental data in Tegzes et. Al (2003). To better illustrate
the flow classifications, the transition and the viscoplastic
regimes were shaded by light and dark gray, respectively.
It is very interesting to find that the surface velocity of most
of the three types of mixture motions (the three U(Y*)
previously summarized) fall nicely into the three zones
separated by the two U,-o correlations. To be more specific,
the dry and the water-submerged mixtures (0 and 0) that
fall in the granular regime exhibited a linear velocity profile
near the surface, composing type-1 flows. The two


7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30-June 4, 2010

immersed mixtures (* and U) and the glycerol-wetted bulk
(A) flowed like a liquid medium, as a type-2 motion, in the
viscoplastic regime. Lastly, the water-wetted mixture (A)
that flowed in the transition phase but closer to the granular
regime show more granular flow characteristics. Only very
near the surface were revealed the liquid cohesion effects
that helped the aggregation of a thin plug layer. However,
the water-immersed mixture motion (0) examined in Fig.7
was found to move in the close vicinity to the viscoplastic
regime, as indicated by the white up-arrow. This may
explain why it showed more liquid-like behaviors, including
the blunt profile across the flowing layer and a diminished
surface strain rate, in Fig. 6.


ition
_ (B)


Drum Speed (RPM)


Figure 7: Mixture surface as a function of drum speed. The
interfaces that separate the transition from the granular and
the viscoplastic regimes are given in (A) and (B).


This close agreement in the two flow classifications
motivated us to reexamine the velocity depth profile in the
flowing layer of each mixture. The flow depth and the bulk
velocity are normalized using the flowing layer thickness as
Y"=(Y-6)/6, and U = U/U, or U/Umax for the cases that
possessed a concave profile with its maximum occurring
beneath the free surface. The result for o=3.96 rpm is
shown in Fig. 8 with the categorization regimes shaded
accordingly. Type-1 and Type-2 bulk motions are well
separated by the two limiting transition flows.

a-05 ( 9 Granularp
-01
-02






-08


8 cP-Watery-Wetted

01 02 03 04 05 06 017 0 09 1
UeUc (crnm/s)
Figure 8: Normalized bulk velocity profiles with flow
classification (0=3.94 rpm).









Further, it is observed in Fig.7 that the water-submerged
mixture converted from the granular into the transition
regime when driven at a lower m = 1.36 rpm (see the left
black arrow). Its normalized U*(Y**) profile is thus
compared to the other mixture motions in Fig. 9(a). The
water-submerged (0) mixture motion that just converted
from the granular regime exhibited a seemingly Type-1 flow
motion. The only evidence showing a liquid-like behaviour
is the slightly diminished surface but this requires more
careful examination in the near future. The water-immersed
mixture (0) is the other bulk falling in the transition regime
but falling closer to the viscoplastic zone on the U,-o plot in
Fig. 7, which may explain why a more concave U*(Y*) was
observed in Fig.9(a).
A last examination was performed for mixture motions at 0
=6 rpm where the resulting bulk motions were well-
separated on the U,-o plot. Consistent conclusions with the
previous remarks can be easily drawn: both granular
flow-like (Type-1) and the liquid flow-like (Type-2)
behaviours were found for bulks that fell in the granular and
in the viscoplasitic regimes, respectively. For bulks that
moved in the transition phase(A, glycerol-wetted), dual
nature behaviours were observed. However, tendency
towards a granular or a viscoplastic flow-like motion cannot
be clearly predicted for its location on the U,-o plot that fell
midway between the two regimes.

(a) m =1.36rpm
0
-0.1
-02


-0.4


(b) 0=6 rpm


U/Uc (cm/s)


UNuc (cm/s)
Figure 9: The normalized bulk velocity depth profile (a) w
=1.36rpm and (b) 0=6 rpm.


7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30-June 4, 2010

Lastly, it is important to note that the two empirical relations,
U, = Ao23 and Bo, rely on coefficients that may change
with respect to the system physical condition, such as the
drum size and the size ratio between the sphere and the
drum radius. This may lead to different flow classification
from the current analysis and further examination is
required to clarify this issue.


Conclusions


In this work, a rotating drum facility and image analysis
methods are introduced to examine the steady motion of
liquid-included granular motions in a thin rotating drum. Via
systematic experiments, we confirmed the speculation
raised here that the U, -o classification rule, namely U, >
20.79o2/3 for a granular flow and U, < 33.590 for a
viscoplastic flow, proposed exclusively for wetted granular
flows may be applied to characterize other liquid-included
mixture motions. The velocity depth profile of a solid-liquid
two-phase flow may be qualitatively predicted by the
knowledge of the drum velocity and the mixture surface
velocity. This latter quantity is always much easier to
measure than the bulk velocity depth profile and thus this
finding may be of some use in many multiphase flow
applications.


Acknowledgements


This study was supported by National Taiwan University
under the project of Excellence Research Program (Grant no.
98R0055-05).


References


Tegzes P., Vicsek T. & Schiffer P. Development of
correlations in the dynamics of wet granular avalanches.
Phys Rev E 67: 051303 (2003)

Jain N., Ottino J.M. & Lueptow R.M. Effect of interstitial
fluid on a granular flowing layer. J. Fluid Mech 508:23-44
k2'"'14)

Courrech du Pont S., Fischer R., Gondret P., Perrin B. &
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7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30-June 4, 2010

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