Group Title: 7th International Conference on Multiphase Flow - ICMF 2010 Proceedings
Title: P3.46 - Thin-gap electrochemical microreactor: effect of operating pressure and electrode surface roughness
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 Material Information
Title: P3.46 - Thin-gap electrochemical microreactor: effect of operating pressure and electrode surface roughness Granular Media
Series Title: 7th International Conference on Multiphase Flow - ICMF 2010 Proceedings
Physical Description: Conference Papers
Creator: Kristal, J.
Zaloha, P.
Jiricny, V.
Publisher: International Conference on Multiphase Flow (ICMF)
Publication Date: June 4, 2010
 Subjects
Subject: surface roughness
gas-liquid
microchannel
electrochemical microreactor
 Notes
Abstract: This contribution reports on the experimental investigation of the effect of the operating pressure and electrodes surface roughness on gas-liquid flow in the thin-gap electrochemical microreactor. For description of gas-liquid flow in the microreactor two hydrodynamic characteristics were selected: flow pattern and bubble size distribution. Experimental data obtained by visualization of gas-liquid flow in microreactor were evaluated by image processing using Matlab Image Processing Toolbox. Our results show that in a microreactor with a very high aspect ratio four flow patterns may exist. Namely, flow without bubbles, dispersed bubbly flow, bubbly flow and churn flow were observed. Presented flow maps indicate the conditions for the respective flow pattern. Results of bubble size distribution confirmed the expected trends; with increasing liquid flow rates the bubble size decreases, and with increasing current density, bigger bubbles are generated. Utilization of the electrodes with lower surface roughness resulted in bigger bubbles, whereas coarser electrodes generated more uniform flow of smaller bubbles. Operating pressure had a dominant effect on bubble size. Already at operating pressure of 1 bar, the electrochemically preferred dispersed bubbly flow was observed for wider range of operating conditions when compared to the atmospheric operation. The effect of operating pressure was significantly stronger than the effect of electrode surface roughness, and appears very promising from the application point of view.
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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Volume ID: VID00532
Source Institution: University of Florida
Holding Location: University of Florida
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Resource Identifier: P346-Kristal-ICMF2010.pdf

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



Thin-gap electrochemical microreactor: effect of operating pressure and
electrode surface roughness


Jiri Kristal, Petr Zaloha and Vladimir Jiricny

Institute of Chemical Process Fundamentals, Czech Academy of Sciences
Rozvojova 135, 165 02, Prague, Czech Republic
kristal aicpf.cas.cz


Keywords: surface roughness, gas-liquid, microchannel, electrochemical microreactor




Abstract

This contribution reports on the experimental investigation of the effect of the operating pressure and electrodes surface
roughness on gas-liquid flow in the thin-gap electrochemical microreactor. For description of gas-liquid flow in the
microreactor two hydrodynamic characteristics were selected: flow pattern and bubble size distribution. Experimental data
obtained by visualization of gas-liquid flow in microreactor were evaluated by image processing using Matlab Image
Processing Toolbox. Our results show that in a microreactor with a very high aspect ratio four flow patterns may exist. Namely,
flow without bubbles, dispersed bubbly flow, bubbly flow and chumn flow were observed. Presented flow maps indicate the
conditions for the respective flow pattern. Results of bubble size distribution confirmed the expected trends; with increasing
liquid flow rates the bubble size decreases, and with increasing current density, bigger bubbles are generated. Utilization of the
electrodes with lower surface roughness resulted in bigger bubbles, whereas coarser electrodes generated more uniform flow
of smaller bubbles. Operating pressure had a dominant effect on bubble size. Already at operating pressure of 1 bar, the
electrochemically preferred dispersed bubbly flow was observed for wider range of operating conditions when compared to the
atmospheric operation. The effect of operating pressure was significantly stronger than the effect of electrode surface
roughness, and appears very promising from the application point of view.


Introduction

Process intensification using the micro reaction technology
is the latest trend in chemical engineering. Hessel (2005)
recently reported the application of microstructured
equipment in many fields of chemical industry. However, in
the field of electroorganic synthesis, microstructured
approach has been intuitively used already since 1960's.
The main reason has been the extremely low conductivity of
the organic solvents resulting in unacceptably high energy
costs when using the classical electrochemical cell
arrangement. The typical representative of a construction
optimized for such a type of process is the so called thin
capillary gap cell. A typical example of a process utilizing
this type of cell represents the electrochemical
methoxylation of 4-methylanisole developed and utilized by
BASF as reported by Lund and Hammerich (2001). Due to
the extremely low interelectrode distance, reaching typically
0.5 to 1.0 mm, this cell may be nearly recognized as a
microreactor. The distinction of the electrochemical
methoxylation process is the hydrogen evolution reaction
taking place at the cathode surface, directly inside the
thin-gap microreactor. Presence of gaseous hydrogen have a
negative effect of the microreactor performance due to
blocking of the active electrode surface by gas bubbles as
reported previously by Kristal et al. (2008). Magnitude of


this effect is in direct relation to the two-phase flow pattern
inside the microreactor where the character of the flow
pattern is determined by operating conditions (amount of
generated gas, liquid flow rate) but also by the surface
roughness of microreactor wall and operating pressure.
The nature of hydrogen evolution is very close to
problematic of pool boiling and also fluid flow in channels
with roughened walls.
In classic works, Colebrook (1939) and Moody (1944)
investigated the effect of surface roughness for conventional
pipes with diameters between 25 and 1524mm and with
relative roughness (e/D, smaller than 5%. Their results
showed that in the laminar regime, the surface roughness
has a very little effect, but in turbulent region roughness
played a major role. The friction factor increased with
Reynolds number and asymptotically reached a constant
value at higher Reynolds numbers. The constant asymptotic
value of the friction factor increased with increasing relative
roughness.
When considering the microchannels, the ratio between the
hydraulic diameter and the geometry of the roughness
profile becomes significantly different from those in
conventional channels. At this scale, the shape spacing and
size of the roughness irregularities have different influence
upon the pressure drop and the overall fluid flow
characteristics (Taylor et al. 2006).






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

that the average radius of the H2 bubbles detaching from the
Ni-PTFE cathodes increased with the PTFE concentration
and therefore with the hydrophobicity of the electrodes.
Presented work aims at determining the effect of surface
roughness and operating pressure on the two-phase flow
patter inside the electrochemical microreactor with
application to electroorganic methoxylation.

Nomenclature


The effect of surface roughness e/Dr 514% on fluid flow
was recently investigated by Taylor et al. (2006). Authors
proposed to consider the effect of flow constriction due to
roughness elements by defining the constricted flow
diameter D,f = D,- 2e. They used constricted flow diameter
for calculating the modified friction factors and Reynolds
number and used these values in a relation similar to
Colebrook equation. When they plotted their experimental
values for s/Dr 514%, the modified Colebrook equation
based on D,, fitted within less than 6% error. Moreover, the
authors proposed six new roughness parameters for more
accurate description of the surface roughness in
microchannels.
Mpholo et al. (2010) carried out a 2D analysis of surface
roughness for prediction of boiling incipience. Authors
analyzed the statistical distribution of the cavities of five
aluminum surfaces with roughness ranging from 0.062 to
12.53 pLm in order to find out if the physical properties of
the cavities could indicate which surfaces are more likely to
initiate boiling earlier than others. Authors conclude that (i)
the polished surface did not seem to have any nucleation
sites to initially trap vapor that would facilitate the release
of bubbles at lower superheat: (ii) for the rough surfaces, the
majority of the nucleation sites were the mini-cavities; and
(iii) the number of active big cavities was insignificant on
all the surfaces except for the roughest one which probably
explains why it needed a substantially lower superheat to
initiate boiling compared to the other surfaces.
Roughness effect on nucleate boiling was studied by
McHale and Garimella (2010). Polished surface
(Ra=0.03 pm) produced periodic bubble generation
originated from the same nucleation site. On the contrary,
no periodic behavior was exhibited with roughened surface
(Ra=5.89 pLm), bubbles were growing separately and the
active site densities were considerably higher. Very fast
bubble coalescence (faster than 1.25x10-4S) occurred
merging many smaller bubbles nucleating at sites on the
roughened surface. Experimental values for bubble
departure frequency, active nucleation site density and
average pool boiling bubble velocity were compared with
published correlations. The latter two characteristics were
well predicted by available correlations but the bubble
departure frequency was not well predicted by any of the
correlations considered from the literature. Authors suggest
that new bubble nucleation correlations should be developed
which incorporate the important effect of surface roughness,
so that recent developments in mechanistic modeling can be
applied for a broad range of boiling surfaces.
Huet et al. (~ll***- studied the oxygen evolution on
electrodes with a porous Ni layer of different roughness.
The analysis of the electrochemical noise indicated that the
dimensions of oxygen bubbles detaching from the
electrodes slightly increased with the deposit surface
roughness. It was not clear, however, whether or not this
increase was associated with the effect of the small (1 pLm)
or the large (10-100 pLm) features on the electrode-bubble
interactions.
Bouazaze et al. (2006) investigated the effect of electrode
surface wetting on the evolution of electrolytic hydrogen
bubbles. Author studied Ni-PTFE composite electrode with
increased roughness. By analyzing the power spectral
density of the fluctuations of the electrolyte resistance,
induced by hydrogen-bubble evolution the authors showed


BSD
CD
EMR
GC
QL


bubble size distribution
current density (A/m )
electrochemical microreactor
glassy carbon
liquid flow rate (ml/min)


Experimental Facility

A schematic diagram of the experimental setup, which was
modified from that used in previous studies Kristal et al.
(2008), is shown in Figure 1. Liquid (reaction mixture) was
pumped with a HPLC pump (ALFA100, Ecomsro, CZ)
trough the electrochemical microreactor to the pressurized
gas-liquid separator. Constant pressure in the whole
apparatus was controlled with automatic pressure controller
(ElPress, Bronkhorst, NL) using pressurized nitrogen bottle
as a pressure source. Two-phase flow was visualized with a
commercial DSLR camera Nikon D70. Acquired images
were subsequently processed with image processing
routines programmed in Matlab Image Processing Toolbox.
Details of image processing can be found in Kristal (2008).


Electrochemical
microreactor


camera



ec


Figure 1: Experimental setup


Experimental EMR had geometry a rectangular channel
with dimensions: length xwidth depth (interelectrode
distance) 150.0 x 10 x 0.1 mm Orientation was vertical.
The inlet was situated at the bottom and the outlet on the top
of the microreactor. The microchannel walls were made of
glass with two pairs of embedded glassy carbon electrodes
(Sigradur G. HTW GmbH, DE). The sketch of EMR is
shown in Figure 2.
The reaction mixture for the electrochemical alkoxylation
was used as a liquid phase. It consisted of 4-methylanisole
(0.01 mol dm ) solution in methanol. Because of low
conductivity of methanol and 4-methylanisol, sodium
perchlorate (0.4 mol dm ) was added as a supporting
electrolyte. Gas phase (hydrogen) was generated
electrochemically on the cathode directly inside the EMR.






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


outlet ~- fixing screws



microchannel
outline \II~distance rod


electrical
connection glassy carbon
electrodes

plastic head




inlet

Figure 2: Sketch of the thin-gap electrochemical
nucroreactor

Investigated range of liquid velocities and current densities
corresponded to the conditions suitable for the
electrochemical reaction (liquid flow rates: 0.2 25 ml/min,
current densities: 100 7000 Am ). Galvanostatic regime
was used.
Wettability of used construction material was assessed by
measuring the contact angle for used liquid phase. The
measurements were carried out by group of Prof. Pohorecki
at WUT, Poland. All measured contact angles were below
5 degrees and indicated good wettability of glass and glassy
carbon.
Experiments were conducted with three electrodes with
different surface roughness. One GC electrode was used as
it was delivered from the supplier-with shiny smooth
surface. Other two GC electrodes were treated with two
emery pastes of grade 800 and 1000, where the higher grade
results in the smoother surface.
Samples of GC electrodes were inspected with the scanning
electron microscope (SEM). Different magnification levels
were used to get detailed information about surface structure.
Illustrative SEM images of electrode surface are shown in
Figures 3, 4 and 5. In the images, the dark regions represent
depressions, the light regions indicate elevations and white
color represents sharp edges on the surface.
Shiny GC electrode had practically no roughness with only
a few very small dents in the surface. Both treated
electrodes had quite uniform structure, and the electrode
surface was slightly disturbed by larger depressions. At the
roughness 1000, the surface was more uniform and the
difference between the elevations and depressions was not
as big as for roughness 800.
We expected that the elevations and sharp edges were places
preferred for the bubble nucleation due to the higher electric
potential. Electric potential was locally increased for two
reasons. First was the electrode edge effect and second, was
the shorter distance between the surface elevation and the
anode. The difference of the electrochemical activity
between elevations and depressions increased with
increasing roughness of the electrode surface.


Figure 4: SEM photo of GC electrode rougimess


1 priOLO or utL eleCuTouc TOUgnItISS


Results and Discussion


Typical images of bubbles generated on electrodes with
different surface roughness are shown in Figure 6. It can be
seen that bubbles rising from the roughened cathode had
much more homogeneous size distribution and have smaller
mean diameter than bubbles rising from the shing cathode,
under the same operating conditions. In case of the shiny
surface, bubble diameter varied widely.






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

atmospheric pressure and different electrode surface
roughness (800 and 1000). The flow map clearly shows that
for studied range of operating conditions the most frequent
flow pattern was bubbly flow. However, under identical CD
and QL, bubbly flow generated on surface roughness 1000
contained significantly bigger bubbles than bubbles
generated on surface roughness 800.
For surface roughness 800, the dispersed bubbly flow was
also relatively common, while for the smoother surface
(surface roughness 1000) the dispersed bubbly flow was
rather suppressed to region with higher liquid flow rates.
Presented flow map also shows that the onset of chumn flow
on surface roughness 1000 is shifted towards lower current
densities, respectively higher liquid flow rates.

closed: roughness 800, open: roughness 1000


O o






Shiny 1000 800
Figure 6: Typical images of bubbles generated on
electrodes with different surface roughness and identical
operating conditions

Images of two-phase flow were visually evaluated
concerning number of visible bubbles, their size and overall
flow character. Based on these characteristics, the two-phase
flow patterns were divided into different categories.
Within the studied range of operating conditions, four
distinct flow patterns were identified:
- Flow without bubbles: bubbles either not present (all
hydrogen was dissolved in the liquid phase) or too
small to be captured by available camera lenses.
Dispersed bubbly flow: homogeneous dispersion of very
small bubbles, the most relevant flow pattern from the
electrochemical application point of view (Kristal
2008).
Bubbly flow: individual bubbles confined between the
front and rear wall with projected diameter
significantly bigger than inter electrode distance.
Chumn flow: complex flow pattern resulting from
multiple bubble coalescence and abrupt gas generation,
and with major part of microreactor filled with gas.


r churn
* bubbly
* dispersed
r no bubbles 4


25 0


E 50

i 25
10
o


g 0 0 g
m 0 O 4 4


V 7J Lu U 4 4
V y o @ O @ PA

y o O O O A
n n o o n A


0 2~ O O @


100 200 400 800 1500 3000 5500
Current densityCD [Alm2
Figure 8: Effect of surface roughness on flow patterns in
thin-gap EMR

Figure 9 shows the experimental flow map for the thin-gap
EMR for studied range of operating conditions (CD and QL ,
surface roughness 800 and the different operating pressure
(atmospheric pressure and 1 bar gauge pressure).
Experimental data for flow rates of 0.2 and 0.5 ml/min were
not available due to construction limitations of EMR.
When operating the EMR under the gauge pressure of 1 bar,
there is a clear shift of flow patterns due to smaller volume
of generated gas at the same current densities. Particularly
noticeable is a shift and broadening of dispersed bubbly
flow at higher QL, towards the highest CD values.
The flow map also indicates a broader region of flow
without bubbles where only the very small bubbles
appeared along the side walls of EMR but no bubbles were
observed in the bulk liquid flow.

closed: atmospheric pressure, open: 1 bar gauge


Illustrative examples of each flow patten
Figure 7.


ar~


~FO
.;; e
;':74p ri
:;.-1"- D
y ;:I:
..li-

".":,-)
~U u
od
o.


e shown in


''


churn
bubbly

sb bubls V


25 0

S10 0
5 o
2 5
U
a 05


v B 0 00
W 0 0 00


Flow without Dispersed Bubbly flow Churn flow
bubbles bubbly flow

Figure 7: Flow patterns in thin-gap EMR

Flow patterns were qualitatively the same for all values of
surface roughness and even for operation under elevated
pressure. However, the onset of a particular flow patten
was shifted, depending on surface roughness and operating
pressure. Effect of surface roughness and operating pressure
on the flow pattern can be easily demonstrated using the
flow maps.
Figure 8 shows the experimental flow map for the thin-gap
EMR for studied range of operating conditions (CD and QL ,


vJ mJ 1+ a *
y O O 2 @ *


* *


* A


- 02E *


100 200 400 800 1500 3000 5500
Current density CD [Alm2]
Figure 9: Effect of operating pressure on flow patterns in
thin-gap EMR












































- ------


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

operating pressure. The effect of elevated operating pressure
on bubble size distribution is clearly evident. Bubbles
generated under elevated pressure were significantly smaller
and had narrower size distribution.

Conclusions

Effects of the electrode surface roughness and operating
pressure on the flow pattern inside thin-gap electrochemical
microreactor with depth of 100 pm were experimentally
investigated. Gas-liquid flow in the EMR was visualized
with digital camera and acquired pictures were evaluated by
image processing. Flow maps and bubble size distribution
histograms were constructed from experimental results.
Four types of flow patterns were observed in the range of
studied operating conditions. According to previous studies,
dispersed bubbly flow was identified as the most relevant
flow pattern from the electrochemical application point of
VieW.
Results showed that flow patterns were qualitatively the
same for all values of surface roughness and even for
operation under elevated pressure. However, the onset of a
particular flow pattern was shifted, depending on surface
roughness and operating pressure. Generally, the electrode
with surface roughness 800 (higher roughness) generated
more uniform flow of smaller bubbles than the surface
roughness 1000.
Results of bubble size distribution confirmed the expected
trends; with increasing liquid flow rates the bubble size
decreased, and with increasing current density, bigger
bubbles were generated.
Operating pressure had a dominant effect on bubble size.
Already at operating pressure of 1 bar, the electrochemically
preferred dispersed bubbly flow was observed for wider
range of operating conditions when compared to the
atmospheric operation. The effect of operating pressure was
significantly stronger than the effect of electrode surface
roughness, and appears very promising from the application
point of view.

Acknowledgements

The authors gratefully acknowledge the support of the
European Commission project No. 0111816-2 IMPULSE.

References

Bouazaze, H., Cattarin, S., Huet, F., Musiani, M. &
Nogueira, R.P. Electrochemical noise study of the effect of
electrode surface wetting on the evolution of electrolytic
hydrogen bubbles. Journal of Electroanalytical Chemistry,
Vol. 597, 60-68 (2006)

Colebrook, F.C. Turbulent flow in pipes, with particular
reference to the transition region between the smooth and
rough pipe laws. Journal of ICE, Vol. 11, 133-156 (1939)

de Gennes, P.-G, Brochard-Wyart, F. & Quere, D.
Capillarity and wetting phenomena: Drops, bubbles, pearls,
waves. New York, Springer (21 1 14)

Hessel, V. Chemical micro process engineering :
Processing and plants. Weinheim, Wiley-VCH (2005)


Bubble size distribution (BSD) is another characteristic that
can clearly demonstrate the effect of surface roughness and
operating pressure on the flow pattern in EMR. Because the
studied microreactor had a very high aspect ratio (width to
depth) of 100, most of the bubbles could be considered as
flat and their size was calculated based on their projected
area in the pictures. Thickness of liquid film between the
bubble and front and rear walls was estimated according to
de Gennes et al. (21is14, to be in the order of units of
micrometers and was neglected against the microreactor
depth and the experimental error. Presented bubble
equivalent diameter was calculated as a diameter of a circle
having the same area as a given flat bubble.
Several BSD histograms were constructed, mainly for the
bubbly flow, using the experimental data for different
surface roughness and operating pressure. Here, only
illustrative examples are presented.


Constant CD = 1500 Alm2

ml/min roughness
-- - 1.0 0 100
-*2.5 1000
------ 1.0 800
2.5 800


14

12
10

6

2


0 2 4 6 8
equivalent diameter [mm]
Figure 10: Histogram of bubble size distribution in
thin-gap EMR for constant CD = 1500 A/m2,
atmospheric pressure and different surface roughness

Figure 10 shows the BSD histograms for the constant
CD=1500A/m2, atmospheric pressure and different surface
roughness. In accordance with flow maps above, the
histograms show that the bubbles generated on the electrode
with surface roughness 1000 were bigger and had broader
size distribution than for surface roughness 800.

Co instant CD = 3000 Alm2


ml/min pressure
2.5 atm
2.5 1 bar


m
m
a,
a 10
n
n
B
o
a, 5
rn
a,
a,
a


~ I~-


0 2 4 6 8
equivalent diameter [mm]
Figure 11: Histogram of bubble size distribution in
thin-gap EMR for constant CD = 1500 A/m2, SURfaCO
roughness 800 and different operating pressure

Figure 11 shows the BSD histograms for the constant
CD=3000A/m2, Surface roughness 800 and different






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


Huet, F., Musiani, M. & Nogueira, R.P. Oxygen evolution
on electrodes of different roughness: An electrochemical
noise study. Journal of Solid State Electrochemistry, Vol. 8,
786-793 (211114)

Kristal, J. Study of gas-liquid flow in the thin-gap channel.
Dissertation, ICPF CAS, Prague, CZ (2008)

Kristal, J., Kodym, R., Bouzek, K. & Jiricny, V
Electrochemical microreactor and gas-evolving reactions.
Electrochemistry Communications, Vol. 10, 204-207
(2008)

Lund, H. & Hammerich, O. Organic electrochemistry. New
York, Marcel Dekker (2001)

McHale, J.P. & Garimella, S.V. Bubble nucleation
characteristics in pool boiling of a wetting liquid on
smooth and rough surfaces. International Joumnal of
Multiphase Flow, Vol. 36, 249-260 (2010)

Moody, L.F. Friction factors for pipe flow. ASME
Transactions, Vol. 66, 671-683 (1944)

Mpholo, M., Mathaba, T. & Bau, H.H. A 2d analysis of
surface roughness for prediction of boiling incipience.
International Joumnal of Heat and Mass Transfer, Vol. 53,
1313-1318 (2010)

Taylor, J.B., Carrano, A.L. & Kandlikar, S.G.
Characterization of the effect of surface roughness and
texture on fluid flow past, present, and future.
International Joumnal of Thermal Sciences, Vol. 45,
962-968 (2006)




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