Group Title: 7th International Conference on Multiphase Flow - ICMF 2010 Proceedings
Title: 11.5.2 - Measurements of apparent wall slip velocity in concentrated suspensions of non-colloidal particles in open channel flow
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 Material Information
Title: 11.5.2 - Measurements of apparent wall slip velocity in concentrated suspensions of non-colloidal particles in open channel flow Particle-Laden Flows
Series Title: 7th International Conference on Multiphase Flow - ICMF 2010 Proceedings
Physical Description: Conference Papers
Creator: Kumar, A.A.
Medhi, B.J.
Singh, A.
Publisher: International Conference on Multiphase Flow (ICMF)
Publication Date: June 4, 2010
 Subjects
Subject: suspension
wall slip
particle image velocimetry
free surface flow
 Notes
Abstract: In this work we have experimentally measured apparent wall slip velocity co-efficient of neutrally buoyant suspension of non-colloidal particles at low Reynolds numbering in an open channel flow. Particle imaging velocimetry (PIV) technique was used to determine free surface velocity for plane and serrated walled channels. The rough walled channel prevents wall slip whereas plane wall showed significant apparent wall slip due to formation of slip layer. By comparing the velocity measurements from these two cases we were able to determine the slip velocity. Experiments were carried out for concentrated suspensions with particle volume fractions ranging from 0.40 to 0.52. The apparent wall slip velocity coefficients are in qualitative agreement with the earlier measurements using other techniques. We have also studied the effect of wall slip on free surface corrugation. The surface roughness for both plane and serrated channel were compared by analyzing the power spectral density (PSD) of the refracted light from the free surface of the channel.
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7th International Conference on Multiphase Flow
ICMF 2010, Tampa, FL USA, May 30-June 4, 2010


Measurement of apparent wall slip velocity in concentrated suspensions of non-colloidal
particles in open channel flow

A. Ashok Kumar, Bhaskar Jyoti Medhi and Anugrah Singh*

Department of Chemical Engineering
Indian Institute of Technology
Guwahati 781 039
Assam, India
anu rah @ iitg.ernet.in; a.ashok @ iitg.ernet.in


Keywords: Suspension, wall slip, Particle image velocimetry, Free surface flow



Abstract

In this work we have experimentally measured apparent wall slip velocity co-efficient of neutrally buoyant suspension of
non-colloidal particles at low Reynolds numbering in an open channel flow. Particle imaging velocimetry (PIV) technique was
used to determine free surface velocity for plane and serrated walled channels. The rough walled channel prevents wall slip
whereas plane wall showed significant apparent wall slip due to formation of slip layer. By comparing the velocity measurements
from these two cases we were able to determine the slip velocity. Experiments were carried out for concentrated suspensions
with particle volume fractions D ranging from 0.40 to 0.52. The apparent wall slip velocity coefficients are in qualitative
agreement with the earlier measurements using other techniques. We have also studied the effect of wall slip on free surface
corrugation. The surface roughness for both plane and serrated channel were compared by analyzing the power spectral density
(PSD) of the refracted light from the free surface of the channel.


Introduction

Suspension of solid particles in viscous fluid are commonly
used in several industrial applications such as paints, polymer,
pharmaceuticals products, drilling mud, and many food
products. At dilute concentrations the suspensions of solid
rigid particles in Newtonian fluid are often modelled as
effective Newtonian fluid having a concentration dependent
viscosity. At moderately high particle concentration the
hydrodynamic interactions between the particles
significantly alter the flow characteristics and we often
observe many interesting phenomena, which are not seen in
the flow of a Newtonian homogeneous fluid under similar
boundary conditions. For highly concentrated suspensions
we also observe apparent wall slip velocity and this has
attracted large number of studies (Yoshimura and
Prud'homme 1988; Kalyan et al., 1993; Aral and Kalyon
1994; Ekere et al., 2001; Nickerson et al., 2005). This wall
slip phenomena is basically occurrence of a relative velocity
between the wall and the suspension at the wall. However,
since the fluid is continuum, even in concentrated
suspensions there is no 'true slip'. It is rather an 'apparent
slip' caused by a region of high velocity gradient adjacent to
the wall compared to the bulk flow. Thus it appears an
apparent slippage of the suspension through a thin liquid-rich
layer at the wall. This layer which is depleted of suspended
particles is called as slip layer. In Rheological measurements
with smooth geometries the effect of wall slip is such that the
measured viscosity (also called as apparent viscosity) is
much lower than the true viscosity of concentrated
suspensions. It is now well established that wall slip or wall


depletion effects are generally observed in the flow of
two-phase liquids in rheometers, in pipe or any channel. In
two-phase flow bounded by a smooth, solid boundary, the
local microstructure is first affected by physical depletion
because the suspended particles cannot penetrate solid walls.
This phenomenon can also be observed if there is no flow
and this is known as static geometric depletion effect. This
could result from steric, hydrodynamic, viscoelastic,
chemical and gravitational forces acting on the solid particles
adjacent to the wall. In many cases, the walls themselves can
repel adjacent particles because of various physico-chemical
forces arising between the particles and the walls, like
electrostatic and steric. When flow takes place in the bulk
fluid, the resulting hydrodynamic and entropic forces can
move the particles away from walls. The presence of large
particles as disperse phase, smooth walls, low speeds or flow
rates and wall and particles carrying electrostatic charges are
some of the reasons which enhance the slip effects.

The overall flow can be divided into two regions, one is the
slip flow operating at the wall, and the bulk flow effectively
seeing a moving wall, but moving normally within it with an
added boundary velocity. The simplest picture which one can
imagine as the consequence of slip is a very thin
continuous-phase only layer left at the boundary, and the
bulk flow with the original concentration. If the slip layer
thickness is comparable with the height of surface
irregularities, then slip would not develop (Soltani &
Yilmazer 1998). It is now well known that to prevent slip at
the wall, roughned and serrated wall surfaces are used
(Barnes, 1995). Figure 1 shows the role played by the surface









roughness in the suppression of wall slip effects. For the case
of plane wall there is a thin liquid rich layer (slip layer) which
is responsible for apparent wall slip. However in case of
serrated wall, the particles can move inside the groove of the
serrations and hence the whole suspension is continuum and
there is no slip layer. Thus if one carries out velocity profile
measurement for serrated wall both true and apparent
velocity profiles will be same. However the smooth wall
measurement will show a different apparent velocity profile.
The motivation of the present work comes from the above
mentioned studies as well as our recent experiments on free
surface flow of concentrated suspensions. In an earlier work
(Singh et al., 2006) it was observed that the velocity profile in
a channel flow is blunted even if there is no particle
migration. In the absence of any significant migration this
could be attributed to the apparent wall slip at the channel
wall. The deviation of velocity profile from the Newtonian
profile increased as the particle concentration was increased.
In the same study the flow structures associated with
free-surface was studied experimentally. The free-surface
velocity for neutrally buoyant suspension of uniform spheres
in a gravity driven inclined channel flow was determined by
PIV technique. The measured velocities showed blunted
profile in the channel. An increase in blunting was observed
with increase in particle concentration D ranging from 0.40
to 0.50. This blunted velocity profile was attributed to the
existence of appreciable slip velocities at the wall of the
channel. It is interesting to note that such phenomena are
observed at low flow speeds where Reynolds number is very
small. The purpose of the present work is to investigate
further the work of Singh et al. (2006) and study the effect of
apparent wall slip velocity on surface corrugation in the free
surface flow of concentrated suspension in open channel. We
have conducted experiment on two channels one with plane
surface and other was serrated surface. Slip effect is
significant in plain surface and serrated surface gives no slip
condition. Jana et al. (1995) determined the apparent wall
slip coefficient of concentrated suspensions of 90p m PMMA
particles in a cylindrical Couette apparatus using the laser
Doppler anemometer system and then extrapolating the
results to the walls. The slip coefficients thereby obtained
were found to be insensitive to the magnitude of the applied
shear rate. However their measurements could be influenced
by lateral migration of particles initiated by the presence of
the wall and non-uniform velocity gradients. The wall slip in
concentrated suspension will be there even if there is no
shear-induced migration. During the flow of suspension the
particles cannot cross the wall and physically cannot occupy
the space very close to wall as efficiently as they can away
from the wall. This wall depletion will always result into a
thin layer of fluid called as apparent slip layer.

We have also adopted the similar methodology (which is
based on measurement of velocity profiles) to determine the
slip coefficient. However our measurements are for open
channel flow using the technique of PIV. We have
extrapolated velocity profiles at different concentration to the
wall of the channel and the difference in velocity between
plane and serrated channel gives the apparent wall slip
velocity.

We have also studied the power spectra of refracted light
from the surface in order to study the length and time scale of


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

corrugation structures at the free surface. The interface of
free surface flow of concentrated suspension is found to be
highly corrugated even at low Reynolds number and this
surface deformation depends on many factors like particle
concentration, surface tension of the suspending fluid and
wall slip effects (Loimer et al., 2002). By analyzing the
power density of the refracted light from the free-surface, the
surface roughness was characterized. Since the relative
illumination intensity is associated with the local inclination
of the surface, study of temporal and spatial intensity spectra
provided valuable information about the wave amplitude and
frequency of the surface deformation patterns. It was
observed that the disturbances at the free surface span over
wide range of frequency and wavelength. By analyzing PSD
results at different concentration in both channels, we try to
investigate further the work of Loimer et al., (2002) and
Singh et al., (2006) on corrugation structure at the free
surface in open channel flow of concentrated suspension.

We have used PIV technique to perform the measurement of
particle velocities at the free surface. Power spectral
densities (PSDs) were computed from the intensities of the
refracted light from the free surface. These PSDs are used to
characterize the surface roughness of the flowing suspension.
Section 2 describes the experimental facilities and
procedures including the optical arrangements and PIV
analysis method. The materials used and method of
preparation is explained in section 3. Section 4 will present
the results from our measurements followed by conclusion in
section 5.


000 0 0 0o 0 0 -- S suspended cl 0 o o o o Suspendedpdlcles
'00 00 0 0 0e
Co o o o o00 0 00 00 o 0 oo0
....... .... ,.. ... silpler I 1t,0 o, a d Pe0oins.ly
..0 s- A A' -ta,+u~4 Peratcl n slip. WVj


ane wall


Serratedwall


Figure 1: Schematic diagram showing the formation of slip
layer at the plane wall (a) and prevention of slip layer in the
serrated walled channel (b).

Nomenclature

a Radius of PMMA particles (pim)
CCD C it ,., I couple device
PIV Particle image velocimetry
PMMA Polymethylmethaacrylate particles
PSD Power spectral density
Greek letters
p Wall slip coefficient
$ Particle volume fraction
y Apparent wall shear rate
pm Micron meter
Subsripts

us Apparent wall slip velocity









Experimental Facilities and procedures

Channel and flow apparatus

Figure 2 shows the schematic diagram of our experimental
setup. The horizontal channel was 43.6 cm long, 2.2 cm wide
and 5.5 cm deep. The plane channel was made of 5 mm thick
glass and the serrated channel with Perspex of same thickness.
For serrated channel the gap and height of asperities were
Imm. A screw pump with variable speed AC motor was used
to pump the suspension in the channel. To dampen the small
fluctuation produced by the screw pump during the flow in
the channel, the upstream and downstream section of the
channel were connected to reservoir each of volume (12.5 X
7 X 3.2) cm and (12.5 X 3 X 3.2) cm respectively. Further, in
the upstream reservoir there was array of baffles to remove
any unsteadiness in the flow. In the figure 2, x is the span
wise direction, y is the flow direction and z is the
gravitational direction. The two ends of the reservoir were
connected via circular tubes of diameter 2cm to the screw
pump, which recirculated the suspension in the channel. The
screw pump was specifically designed to handle suspension
of large particles. The speed of the screw pump could be
adjusted to get the desired flow. The suspension in the
channel was filled to a level such that the free surface in the
x-y plane was about 2 cm from the bottom wall. The optical
arrangements to capture images for PIV analysis is also
shown in figure 2. An argon ion continuous laser from
spectra physics (actual power 1 W, k = 514 nm) was used as
light source. Two mirrors were used to reflect the beam,
which was then used to generate a horizontal light sheet
illuminated from the downstream side of the channel (shown
by the shaded region in the x-y plane of the figure 2) using
cylindrical lens. The images were captured using a 1360 X
1024 pixel CCD camera (PixFly HiRes from PCO) in
conjunction with a macro zoom lens (Navitar). The camera
can either operate in fixed mode (video mode) or in double
shutter mode to capture images. In our experiments the
camera was operated in fixed mode with frame rate of 19
frames/sec and the duration between subsequent images was
52 ms. The maximum (centreline) velocity in the channel
used in our study varied from 0.5 cm/s to 2.5 cm/s. The
maximum wall shear rates reached in these experiments were
less than 10 s 1


PC & Frame Grabber


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



Thus, for particles with a typical radius, a, of 200 pm and a
fluid with viscosity, v, of 150 cP, the Reynolds number on
particle size was O( ~10 3 ) and yet smaller if effective
viscosity of suspension is considered.

PIV image analysis method

Particle image velocimetry is a non intrusive, full field
optical measuring technique based on image processing.
This technique is used for instantaneous measurements of
the velocity field and this has been applied to many kinds of
flows. In any PIV experiments, the fluid of interest is seeded
with neutrally buoyant tracer particles, which are
illuminated by a light source (usually a laser sheet for better
illumination of tracer particles). The images of these tracer
particles at different times are recorded with CCD camera.
Displacement of particles between two successive images
ascertains the motion of the fluid (Adrian et al., 1995). The
details of PIV analysis can be found in our earlier work
(Sing et al., 2006). The free surface was visualized by
seeding the flow with hollow glass particles of diameter 10
- 25 pm supplied by ICI limited. Figure 3 shows a
representative PIV photograph of the free surface in x y
plane. With the lens operating at magnificent of 0.7 the view
of the flow field (15.5 X 11.5 mm) was captured. The
captured images were saved in 680 X 512 pixels, 12 bits
format grey scale images on a computer via frame gabber.
To calculate the free surface velocity from pair of images
we have used the PIV analysis software PIV SLEUTH
(Christensen et al., 2001). The image pairs were
interrogated using two-frame cross correlation technique of
Adrain et al., (1995). In our experiments the time difference
between two images was 52 ms when images were recorded
with camera working in fixed mode of 19 frame/sec. The
spot size for flow field interrogation was 128 X 128 pixels
with 75% overlap between interrogation spots. Thus the
size of the interrogation window was about 729 pm. The
size of the interrogation window was estimated by
processing the images with interrogation window sizes
varying from 32 X 32 pixels to 256 X 256 pixels and
choosing the size that resulted minimum spurious vectors.
This interrogation resulted in, approximately, 13 rows and
14 columns of vectors for each image. The good quality
images insured that very few wrong vectors were computed.
Vectors with low signal to noise ratio were removed and
replaced with interpolated vectors from the nearest points.


Mirror


Figure 2: Schematic of the experimental setup and optical
arrangements for PIV study.


X (mm)
Figure 3: A sample PIV image of tracer particles at the free
surface of the channel.










Preparation of suspension

All the experiments were carried out with neutrally buoyant
suspension which required density matching of fluid and
particles. In our study the particles used in preparing the
suspension were PMMA spheres of mean diameter 200 pm.
The density of particles were 1.18 gm/cc. To prepare a
density matched suspending fluid we used mixture of 74%
glycerol and 26% water (weight %). The suspending fluid
had a viscosity of approximately 150 cP and its surface
tension value was measured to be 60.4 mN/m. We prepared
approximately 1000 ml of suspension which was needed to
fill the flow apparatus. To prepare the suspension requisite
amount of particles and liquid were added in beaker and
stirred vigorously to achieve homogeneous mixing and
dispersion of the particles. However, during the mixing small
air bubbles were formed which needed to be removed. This
was achieved by keeping the suspension under vacuum for 1
day, allowing the bubbles to rise up. Suspension cleared of air
bubbles was then gently transferred in to the channel.


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

suspension with particle concentration of 40%. It can be
observed that the scaled velocity profiles are similar at
different flow rates. This is true for both plane and serrated
channel. This insured that the measured velocity profile at the
above mentioned location was fully developed for
suspension flow as well. We obtained similar behaviour for
higher concentration of particles (not shown here). It is to be
noted that the velocity profile for suspension flow is not
parabolic as also observed in the studies of Singh et al.
(2006) who obtained similar profile in the absence of any
appreciable migration. In the present experiments also no
significant particle migration was expected. Moreover, the
mixing of suspension in the screw pump and the small length
of channel insured that lateral migration of particles across
the channel remained minimal. To verify this we had
conducted one experiment in which a small fraction of the
suspending PMMA particles were dyed in black colour. The
image of these particles showed uniform concentration
across the whole channel width. This image of these particles
showed uniform concentration across the whole channel
width. This indicates that there is no appreciable migration in
the x-y plane for which we report the velocity profiles.


Results and Discussion


Wall slip co-efficient measurements

To find the location where the velocity profile was fully
developed beyond entrance effects, we measured velocity of
suspending fluid at different location for both plane and
serrated channel. We found that at 23 cm from the channel
entrance the velocity profile was fully developed as all the
profiles coincided. Therefore, all the velocity measurements
were carried out at this location for both the channels. Figure
4 shows the comparison of experimentally determined mean
y- velocity profile for both the channels with the analytical
value (parabolic profile). To get the mean velocity profiles,
an average of 100 velocity vectors was taken which were
obtained by cross-correlation analysis of 100 consecutive
pairs of images. A very good agreement ensured that the
present concentration of tracer particles produced very few
erroneous velocity vectors and the profile is indeed fully
developed at the measurement location.


1

0.8

S0.6

.0.4

0.2 Analycal
o Experimental (Plane Channel)
Experilental (Serratrd Channel)
0 1 2 3 4 5 6 7 8 9 10 11
X(mm)
Figure 4: Fully developed mean y velocity profile for
pure suspending fluid for plane channel and serrated channel.


Figure 5 shows the y-velocity (scaled with the centre-line
velocity) profile at various centreline velocity (Vmax) for


.8

.6

.4
SVmax=0.0126 m/s
.2 Vnma=0.018 m/s
O Vmax=0.0222 m/s

0'1 2 34 56 7 89 1011
X (mm)


: .-.---



.6 a
,
o Vmax=0.0036 mis
Vma=O.0O144 mis
Vmax4.0167 mis

1 2 3 4 5 6 7 8 91011
X (mm)

(b)


Figure 5: Mean y velocity profile across the channel at
various centreline velocities for suspension of 40%
concentration. (a) Plane channel (b) Serrated channel. The
particle size was 200 pm.

In figure 6 we present the comparison of velocity profiles for
plane and serrated walled channel for various concentrations
of particles. It is to be noted that we were not able to measure
the velocity very close to the wall due to large size of the
interrogation windows. Besides this, due to curvature effect
the tracer particles close to wall were not illuminated
properly by the laser sheet (Figure 3). When small
interrogation window size (32 X 32 pixels) was chosen for
PIV analysis we obtained erroneous velocity vectors. For the
interrogation window size of 128 X 128 pixels correct
velocity vectors were obtained. Therefore to obtain the wall
velocity we extrapolated the measurements points by fitting a
cubic spline curve. When the curve for serrated channel is
extrapolated to the wall it gives wall velocity close to zero,
however for plane channel this value is positive. The
difference between the two curves (plane and serrated wall)
gives the wall slip velocities for that particular concentration
of suspension. One can argue the justification of the choice of
this curve fitting when the velocity profile is not quadratic.






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


Though analytical nature of the velocity profile curve for
suspension flow is not available, the present choice of curve
fit closely matches with the experimental measurements. It
can be also observed that there is significant difference
between the velocity values for plane and serrated channel
for the first measurement location close to the wall. This
difference is close to the difference between the extrapolated
values at the wall. Any deviation will not change the results
qualitatively. Thus we propose that the value of wall slip
velocity measured by extrapolation to the wall is justified.
The wall slip coefficients were determined from the
following expression given by Jana et al., (1995),


=us


Where, us is the apparent wall slip velocity, y is the
apparent wall shear rate (determined from the slope of
velocity profile of the plane channel) and a is the radius of
PMMA particles.


0.8
S. \ t

0.2 -----Pinur Cinr i
- *s l au l
o 1 2 3 4 5 6 7 8 9 1 11
X (mm)
(a)


--s--- Plate Chnue
1 2 3 4 5 6 7 8 9 10 11
X (mm)
(c)


o "- 4--0.45

0-6
/ /
0.4
0.2 Pb
S1 2 3 7 8 9 10 11
X (mm)


S1 2 3 4 S 6 7 8 91011
X (mm)


Figure 6: Mean y velocity profile across plane and
serrated channel at various concentrations (a) 40%; (b) 45%;
(c) 48%; (d) 50%. The dashed lines are cubic spline fit of
experimental data.

Figure 7 shows comparative plot of dependence of apparent
slip co-efficient on particle concentration with the
experimental measurements of Jana et al (1995) as well as
theological studies of Ahuja and Singh (2009). There is
qualitative agreement with the previous measurements.
However, the slip coefficients from present measurements
are consistently higher than Jana et al. (1995). There could
be several reasons for this observation. The PMMA
particles (90 im) in the experiments of Jana et al. were
much smaller compared to ours. Besides, the suspension in
their study was not neutrally buoyant due to mismatch
between fluid and particle densities. The viscosity of
suspending in our experiments was 150 cp whereas Jana et
al. worked with suspending fluid of viscosity 240 cp. The
viscosity of suspending fluid in the experiments of Ahuja
and Singh (2006) was 320 cp and the mean particle diameter
was 165 pm. It is well known that the viscosity of the
suspending fluid affects the slip behaviour of the suspension
and a smaller viscosity gives rise to a greater slip velocity
(Ahuja & Singh 2009). These results also indicate that the
wall slip increase with increase in particle size.


Figure 7: Plot of apparent slip co-efficient with particle
concentration.

Free surface corrugation

Loimer et al. (2002) have studied the free surface during the
simple shear flow of concentrated suspensions of small
inertial-less particles in a viscous fluid and observed the
development of corrugation on the surface. It was observed
that the roughness of the surface disturbances depends on
the particle size, particle concentration and on the surface
tension of the suspending fluid. Subsequent to these
findings Timberlake and Morris (2005) and Singh et al.
(2006) have carried out experiments to characterize the
surface corrugation by the analysis of the spectra of the
refracted light from the free surface. They have shown that
flow structures of many length scales are present. It was
also observed that as the particle fraction increases the
autocorrelation in flow direction declines faster until a
critical fraction is reached, thereafter the autocorrelation
function decays slowly. In the same study Singh et al.
observed that as the concentration increases the blunting of
velocity profiles across the channel increases. Now it is
clear that in the absence of significant particle migration the
velocity profile indicates the presence of slip between the
fluid and particle velocities near the wall of the channel.
Therefore we have performed experiments to study whether
wall slip affects the surface corrugation patterns or not. The
surface images were taken by placing the camera above the
surface and illuminating the free surface using a cold light
source (Thorlab). The light source was placed at an
appropriate angle so that it reached the camera lens after
refraction from the free surface. The corrugated surface
refracted the light depending upon the local free surface
orientation.

Power spectral density of image intensity for both temporal
and spatial directions provide indirect estimate of surface
corrugation since the exact relation between the surface
curvature and intensity of the images is not known (Loimer
et al., 2002; Timberlake and Morris 2005). The near surface
particle fluctuation causes deformation of the interface.
When the deformation relaxes, the energy contained within
it is released back in to the fluid. This may further affect the
surface topography elsewhere. For temporal measurements
photographs were taken at a frame of 19 frames / sec. The
power spectral density (PSD) of image intensity values was
computed using fast Fourier transform similar to Singh et
a. I i 2 11 .I A total of 256 frames were taken to get the PSDs.
Figure 8 shows the comparison of temporal PSD at different


P-*. Present work
25 --Ja etd. (1995)
-*-Ahuja and Sing (2009) P
20

15 ..,

10 ..... e



0,5 0.4 0,- --
0.35 0.4 0.45 0.5 0.o









concentration for both plane and serrated channels. These
plots show large peaks at regular intervals indicating the
presence of flow structures at multiple time scale. In
addition to this the nature of the plots are same for both
channels at all concentration studied. This indicates that
wall slip may not have any apparent effect on the surface
corrugations. The length scale associated with the flow
structures can be estimated by using the Taylor hypothesis
i.e. multiplying the time scale with the local average
velocity at the position.


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

particle again follow ordered motion due to crowding effect.
There exists a critical particle fraction value when the
fluctuations are strong enough to produce wide spectrum of
uncorrelated flow structures. Thus our study concludes that
wall slip does not change the nature of surface corrugation
patterns observed during free surface flow of concentrated
suspensions.


---=0.45
S-- -*--- 0.48
-.- 40.5




0.1 0.2 0.3 0.4
A x(cm)


(a)
Figure 9: Normalized spatial auto -
direction for (a) plane (b) serrated channel.


^ -- =0.4
3 s Z' ---=0.45
.3 *=0.48
.2_ -=0.5
3.2 .0 0 PL o 0.2

.1

0 0.1 0.2 0.3 0.4
A y(cm)


0 5 10 0 S 10
f (HZE) f(Z
(a) (b)
Figure 8: Temporal PSD at different particle concentration
for (a) plane and (b) serrated channel..

For spatial PSDs measurements in flow direction (y) an area
of full image height, 512 pixels was taken. The PSDs were
averaged for several uncorrelated frames. Similarly for
PSDs perpendicular to the flow direction (x-direction) the
area of full image width, 680 pixels were taken. From the
same data the auto-correlation functions were computed.
These correlation functions represent how the flow structure
at a location is correlated with that at some downstream
location. In figure 9 we have compared spatial
auto-correlation in x directions for suspensions with particle
fractions 0.40, 0.45, 0.48 and 0.50 for both plane and
serrated channel. The corresponding auto-correlation in y
direction is shown in figure 10. The plots for different
concentration reveal that the flow structures uncorrelated
faster for particle concentration of 0.40 & 0.45 compared to
the higher particle concentration. However the with particle
concentration of 0.50 we observe that the auto-correlation
decays slower for both types of channels. This observation
is in agreement with the earlier findings of Loimer et al.,
(2002) and Singh et al., (2006) who report maximum
disorder at particle concentrations between 0.40 and 0.45.
The rate of decay of auto-correlation is related to the flow
structures. At low concentration the particle fluctuations are
not strong enough and the flow structures convect with the
mean flow. On the other extreme i.e. when the particle
fraction approaches to maximum packing fraction, the


Ax(cim)

(b)
correlation in x


0.1 0.2 0.3
A y(cm)


Figure 10: Normalized spatial auto correlation in y
direction for (a) plane (b) serrated channel.

Conclusion

We have measured the apparent wall slip velocity co-efficient
of concentrated suspension in channel flow with the tool of
particle image velocimetry. These results are compared with
the earlier findings of Jana et al. (1995) using laser Doppler
velocimetry and theological measurements of Ahuja and
Singh (2009). It is observed that the wall slip velocity varies
linearly with shear rate. The slip coefficient is low at
moderate concentration but increases rapidly as higher
concentration is reached. These results are in qualitative
agreement with the earlier works. The effect of slip velocity
on surface corrugation was studied by analysis of the spectra
of the spectra of the refracted light from the free surface. It is
found that the normalized spatial and temporal spectra are
similar for both plane wall and serrated wall channel. The
spatial auto-correlation in flow and span-wise directions for
plane and serrated channel also didn't show any significant
variation to make any conclusive observation. Thus it
appears that the wall slip affects the velocity profile close to
the wall as well as blunting of profile but this has no apparent
effect on the surface corrugation patterns.

Acknowledgements

The author acknowledge financial support from DST, India
through the project no. SR/S3/CE/38/2006.






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




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