5th International Conference on Multiphase Flow, ICMF’04
Yokohama, Japan, May 30–June 4, 2004
Paper No. 308
Wet Particles in Granular Sheared Flows
Wen-Lung Yang1, Shu-San Hsiau2
1: Dept. of Mechanical Engineering, National Central University, Chung-Li, Taiwan, ROC, s9343010@cc.ncu.edu.tw
2: Dept. of Mechanical Engineering, National Central University, Chung-Li, Taiwan, ROC, sshsiau@cc.ncu.edu.tw
Abstract We have studied the transport properties of wet granular materials in shear cell apparatus. If the
particles of flows are wet, the flows become more viscous and the liquid bridges between particles. The
dynamic liquid bridge forces are considered as the cohesive forces between particles to restrict the
movements of particles. The cohesive forces make the particles stick tighter with each other and hamper the
movements of particles. The mixing and transport properties are influenced seriously due to the amount of
moisture in the flow. This paper discusses a series of experiments performed in a shear cell device with five
different moisture contents using 3-mm glass spheres as granular materials. A high-speed camera recorded
the motions of the granular materials. Using the image processing technology and particle tracking method,
the average and fluctuation velocities in the streamwise and transverse directions could be measured. The
self-diffusion coefficient could be found from the history of the displacements of particles. The self-diffusion
coefficients and fluctuations in the streamwise direction were much higher than those in the transverse
direction. Three bi-directional stress gages were installed to the upper wall to measure the normal and shear
stresses along the upper wall. For the wetter granular material flows, the fluctuation velocities and the
self-diffusion coefficients were smaller.
1. Introduction
Granular materials are collections of discrete solid particles dispersed in a vacuum or
interstitial fluid. The voids between particles are filled with a fluid such as air or water. Therefore,
the flow behaviors of granular material can be treated as a multiphase flow. Granular flows are
widely found in nature, such as ice flow, soil liquefaction, landslides and river sedimentation. In
industries, granular flows are widely found in the mixing and transport processes of foodstuffs, coal,
pellets, metal mine and so on. In chemical industry more than 30％ of products are formed as
particles (Shamlou, 1988). All granular flows are highly dissipative. The energy supplied to a
granular flow, through vibration, gravity, or shearing is rapidly dissipated into heat. Thus, work
must constantly be done on the system to maintain a granular flow.
The dominant mechanism affecting the flow behavior is the random motions of particles
resulted from the interactive collisions between particles (Campbell, 1990). Because of the random
motion of particles in a granular flow is analogous to the motion of molecules in a gas, the
dense-gas kinetic theory (Savage and Jeffrey, 1981; Jenkins and Savage, 1983; Lun and Savage,
1984; Jenkins Richman, 1985) and molecular dynamic simulations (Campbrll, 1989; Lan and
Rosato, 1995) are borrowed to analyze and model the granular flow behavior.
Due to the difficulty in measurement of granular temperature, there were relatively few
experimental studies about this important quality. Fiber-optic probe technology was employed by
Ahn, Brennen and Sabersky (1991) and Hsiau and Hunt (1993) to measure the fluctuation, but only
in the bulk flow direction. The image technology and the autocorrelation method were used by
Natarajan, Hunt and Taylor (1995) to study the two-dimensional granular temperatures of granular
material flows in a vertical channel. Hsiau and Jang (1998) used the similar technology to measure
the flow behavior in a shear cell. The anisotropic distribution of fluctuations were clearly
demonstrated in the above three experimental studies.
The presence of small amount of interstitial fluid in the system introduces another degree of
complexity due to the cohesive forces between particles in addition to the core repulsion force and
the friction force present for dry granular matter. An increase in repose angle is the most well
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5th International Conference on Multiphase Flow, ICMF’04
Yokohama, Japan, May 30–June 4, 2004
Paper No. 308
known effect of the presence of interstitial fluid in a granular system and has become a topic of
current interest (Tegzes et al., 1999; Halsey and Levine, 1998). The interstitial fluid also alters the
percolation of particles, and the particles tend to behave as clumps rather than individual grains.
The research about wet particles is more important at present. When the particles have a little
amount of water, they would gather together and hinder the movements of themselves. There are
plenty of indications, both in laboratory and in industrial situations, that other perturbations can
complicate thing and consume our ability to model the behavior of “dry granulars” as we have
defined them earlier (Hsiau and Shieh, 1999). Ambient humidity, for instance, can cause serious
disruptions by creating clumps of particles that are more or less mobile. We know from common
experience that wet sands could be fairly cohesive, whereas dry sands crumble apart readily. Due to
the appearance of liquid bridge between particles, the capillary force should be considered as an
important force effecting the motion behaviors of the granular system. Calculating the capillary
force that keeps two wet spheres in contact is far from trivial. Several methods have been proposed
to avoid the difficulties associated with solving the Laplace-Young equation (Erle et al., 1971; Lian
et al., 1993).
The Couette granular flow was the simplest and very suitable for fundamental research. Some
examples of the related experimental studies are Savage and Mckeown (1983), Savage and Sayed
(1984), Hanes and Inman (1985), Johnson and Jackson (1987), and Wang and Campbell (1992).
Most earlier experiments measured only the averaged stresses by transducers and assumed that the
flow in the cell is a simple shear flow. However, the assumption should not be true in a shear cell
because of gravitational force as demonstrated in the study of Hsiau and Shieh (1999). In our earlier
research (Hsiau and Yang, 2002; Hsiau and Yang, 2004), we started to use the bi-directional stress
gages to measure the normal and shear stresses along the upper wall. We studied the granular flows
with different wall friction coefficients and solid fractions. The self-diffusion coefficients of
granular flows increase with increasing the wall friction coefficients. However, they are decrease
with increasing the solid fractions. This paper focuses on the effect of the presence of moisture. We
performed experiments in a shear cell device that supplied by a constant external energy with five
different moisture contents. The present paper employed the image technology and particle tracking
method to investigate the granular flow transport properties in the shear cell. Three bi-directional
stress gages were buried in the upper wall to measure the normal and shear stresses of granular
materials along the surface. The dependence of the measurements on the moisture content will be
discussed.
2. Setup
The experiment materials in this study are soda lime beads which have an average diameter dp
of 3 mm (standard deviation of 0.04 mm and particle density of 2490 kg/m3). There are 5%
identical red soda lime beads serving as tracers. The average solid fraction  of the test is calculated
from the particle mass (1.5 kg in this paper) divided by the particle density and the test section
volume. In this study, we control the average solid fraction  to a value of 0.6285. A certain amount
of water and tested particles were weighted by an electronic scale with accuracy of 0.001g. The
water and the particles were put into a sealed jar. Then, we shook the sealed jar to mix the water and
particles. The wet particles were put into the shear cell apparatus. We also measured the weight of
sealed jar before and after putting the wet particles. Therefore, we know how much water in the
granular flow and control the moisture content. The accurate values of the masses of water and
particles which were put in the shear cell could be decided. The moisture content V* would be
calculated.
In this study we use the annular shear cell apparatus which schematically shows in Fig. 1. The
experimental setup has a rotation bottom disk (outside diameter: 45.00 cm; thickness of 4.50 cm)
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5th International Conference on Multiphase Flow, ICMF’04
Yokohama, Japan, May 30–June 4, 2004
Paper No. 308
which is driven by a 3 hp AC-Motor. A tachometer we used to measure and control the rotation
speed of the bottom disk. In this study, the AC-Motor supplies a constant energy into the shear cell.
The bottom disk is made of plexiglass for visualization purposes. An annular trough (inside
diameter: 31.67 cm; outside diameter: 42.02 cm) was cut in the bottom disk. The stationary upper
disk was inserted into the trough after the wet granular materials were put in the test section. A dial
indicator is installed in the apparatus to measure the adjustable height h of the test section.
420.2 mm
Motor
316.7 mm
Fixed steel
shaft
Upper disk
Assembly
Stress gage
Acrylic bottom
disk
45.0mm
Shear
space
h
a layer of particles
adhered for generating
shear force
51.75mm
V-belt
Bottom disk
bearing assembly
Bottom disk
assembly
Steel base plate
Fig. 1. Schematic drawing of the Couette shear cell experimental apparatus.
There are three bi-directional stress gages been installed along the upper wall to measure the
normal and shear stresses, shows as Fig. 1. The detecting surfaces of the stress gages are even with
the upper wall. The idea of the stress gage is based on a simple ring dynamometric element which is
provided with semiconductor strain gages. The normal and shear stresses are realized by two
different wiring systems of the strain gages, and we can measure the normal and shear stresses in
the same time in this study.
The stress gage utilizes two different full bridge semiconductor strain circuits to measure both
stress components simultaneously and independently. The diameter of the measuring surface of the
gage is 2.0 cm. The measuring surface can be replaced with the same wall material as the upper
surface of the test section. A stable voltage of 10 Volts is supplied to each stress gage by a DC
power supply. When the stress gages sense the normal and shear forces from the granular materials,
the voltage signals are translated from the gages to a personal computer through a data acquisition
card (Advantech PCL-818HG). A series of calibration tests were carefully done in two directions
through dead weights and then the calibration lines (straight lines) representing the dependences of
the output voltage signals on the normal and the tangential loads on the gages can be determined.
The accuracy of the pressure gages is over 99%. The normal and shear stresses are then determined
from the average of the signals from the three stress gages.
In this study, the influence of the moisture conditions on the flow behaviors is investigated.
The friction coefficients between particles and walls and among particles were measured by a
commerial Jenike shear tester. Plotting for each of these the shear stress against the normal pressure
determines the straight lines through the origin of which the slopes define the internal friction angle
and wall friction angle. However the straight line of the internal friction angle will touch the y-axis
and indicate a value. The value is the cohesive force between particles.
The granular flow in the test section is assumed to be two-dimensional with streamwise
(horizontal) direction as x-axis and transverse (vertical) direction as y-axis (upwards is positive).
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5th International Conference on Multiphase Flow, ICMF’04
Yokohama, Japan, May 30–June 4, 2004
Paper No. 308
Because of the visualization limitation, only the flows adjacent to the outer surface of the annular
trough in the bottom disk could be recorded and analyzed. The velocity of the lower wall u0 could
be calculated from the product of the rotational speed of the bottom disk and the outside radius of
the trough. In this paper, we controlled the input energy been a constant and measured the rotational
speed. The rotational speed u0 was fixed at 0.88 m/s.
A high-speed camera recorded the motions of the granular materials. Using the image
processing technology and particle tracking method, the average and fluctuation velocities in the
streamwise and transverse directions could be measured. The flow motions were recorded by a
high-speed camera. In this study, the images were grabbed at a speed of 500 frames per second. The
autocorrelation technique was employed to process the stored images and to decide the shift of each
tracer particle in every two consecutive images. The details of the autocorrelation process can be
referred to the paper by Hsiau and Shieh (1999).
The height of test section was divided into 10 regions. The ensemble average velocities in
horizontal and vertical directions, <u> and <v> in each region were averaged from about 250 tracer
particles (8500 frames):
N
 u 
u
k 1
k
;
N
(1)
N
 v 
v
k 1
k
,
(2)
N
where k represented the kth tracer particle, N was the total number of velocities used for averaging
the mean values, and uk and vk are the velocities of the kth tracer particle measured from the two
consecutive images containing the kth tracer particle. The fluctuation velocities in the two directions
were calculated by:
N
 u  2 1 / 2 
 (u
k 1
k
N
N
 v  2 1 / 2 
  u ) 2
 (v
k 1
k
;
(3)
  v ) 2
.
(4)
N
Since the current study followed the auto-correlation technique developed by Hsiau and Shieh
(1999) which took into consideration of the correlation values of gray level derivatives, the
experimental errors of the velocities were reduced within 1.5%.
The Granular Bond Number Bog was defined as the ratio of the maximum capillary force Fc
and the weight of the particle, W (Nase et al., 2001). It was somewhat reminiscent of the Bond
Number in fluid mechanics, so by analogy was referred to as the Granular Bond Number Bog,
F
2R
3
Bo g  c 

.
(5)
4
W
2 R 2 g
3
R g
3
where R was the radius of particle (R = 0.0015 m), the fluid surface tensionγwas a value of
7.34*10-2 N/m (Munson et al., 2002), and ρp was the density of the solid (ρp = 2490 kg/m3). In
this study, the Granular Bond Number was a constant (Bog = 2.003256). The cohesive effect
should be considered with Granular Bond Number greater than 1 (Bog > 1)(McCarthy, 2003) In
McCarthy’s research, the Collision Number Co was defined as the ratio of the maximum cohesive
force Fc and the collisional force FBg,
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5th International Conference on Multiphase Flow, ICMF’04
Yokohama, Japan, May 30–June 4, 2004
Paper No. 308
Co 
Fc

FBg
2R
(6)
.
2


du
s 2 R 4  
 dy 
2
where λ was a constant and du/dy represented the shear rate. We could know the degree of
collision from the Collision Number.
The velocity fluctuations induce the self-diffusion in granular shear flows. Einstein (1956)
first employed the concept for analyzing the diffusive phenomena of suspended particles
undergoing Brownian motion in a liquid. This technique was used by Savage and Dai (1993) and
Campbell (1997) to investigate the diffusive behavior of granular flow systems through computer
simulation. The self-diffusion coefficient was defined as
lim  x i x j  2 Dij t
(7)
t 
where xi and xj are the diffusive displacements in directions i and j. Similar concept was
employed by Natarajan et al. (1995) to study experimentally the granular self-diffusion in a
1-m-high vertical channel. However, it was very difficult to record the movements of the tracer
particles in a rotated shear cell since the particles moved out of the view window of the CCD
camera in a very short time. The idea of “periodic cell” used in computer simulation (Campbell and
Brennen, 1985) was introduced in the experiments by Hsiau and Shieh (1999). In this experiment,
when a tracer particle moved out of one image, the time counter for this particle was paused. The
computer program would then search the following images, until the other tracer particle was found
in the inlet with the same channel height and the same velocities as the former tracer. The path of
this new tracer particle from the image inlet was then treated as the continuous movements of the
former tracer particle. The mean-square diffusive displacements <xx>, <yy> and <xy>
were averaged from about 200 tracer particles taken from 7000 to 9000 frames. The experimental
errors were mainly resulted from the uncertainty in determining the centroid of a particle. The errors
of diffusion coefficients Dxx and Dyy were estimated beyond 2% and 5% respectively.
3. Results
The five tests in this study were done for a total granular mass of 1.5 kg and a fixed channel
height of 1.6 cm. The average solid fraction of the current setup was 0.6285. We controlled the
input energy been a constant. The lower wall velocity u0 was fixed at 0.88 m/s. The dimensionless
liquid bridge volume, V* = Vl/(Vl +Vp), was used as a control parameter in this paper, where Vl was
the volume of water and Vp was the volume of the particles. In this paper, we used five moisture
contents (V* = 0, 0.008, 0.017, 0.025 and 0.033). Fig. 2(a) shows the distributions of the ensemble
average velocities in the streamwise and transverse directions, <u> and <v>, with different moisture
contents. The transverse velocities are close to 0 as expected because there is no vertical bulk
motion in the channel. The streamwise velocity decreases with the height and is greater for the case
with wetter granular flows (greater V*). Slip velocities exist at the lower and upper walls. The upper
slip velocities are about 61% to 80% of the lower wall velocities. Due to the gravity effect, there
exists a “solid-like region” (Zhang and Campbell, 1992) in the lower half of the channel with faster
and more uniform velocities in the streamwise direction. The shear rate is higher in the upper
section where is called the “fluid-like region” (Zhang and Campbell, 1992) or “shear layer”
(Aidanpää et al., 1996). From Fig. 2(a), the values of the shear rates in this region deviated
significantly with different moisture contents. For the test with greater moisture content, V*, the
velocity gradient is lower since the wetter particles (greater V*) can generate higher cohesive forces
between the particles resulting in the lower shear rate. The energy of flow is dissipated highly due
the frictional forces between the particles.
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5th International Conference on Multiphase Flow, ICMF’04
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Paper No. 308
The distributions of the fluctuation velocities in both directions for the five tests are shown in
Fig. 2(b). It indicates that the fluctuation velocities in the streamwise direction are much higher than
those in the transverse direction. The distribution of fluctuation is not isotropic as assumed in the
dense-gas kinetic theory (Campbell, 1990). The explanation about this anisotropic phenomenon can
be referred to Hsiau and Shieh’s paper (1999). Because of the increase in the shear rate (d<u>/dy)
with the height, the fluctuations also increase with the channel height, as shown in Fig. 2(b). The
influence of the moisture content on the fluctuations is significant. The streamwise and transverse
fluctuation velocities along the upper wall with moisture content of 0 are over two times and three
times of those with moisture content of 0.033. The deviation is mainly resulted from the different
shear rates generated in different moisture conditions. Because the viscous and liquid bridge forces
between particles of the wetter granular flows are greater which restrict the flow motions, the
fluctuation velocities of wetter granular flows are smaller.
1
1
(a)
(b)
0.8
Scaled Height, y/h
Scaled Height, y/h
0.8
0.6
u0=0.88 m/s
<u> V *=0
<v> V *=0
<u> V *=0.008
<v> V *=0.008
<u> V *=0.017
<v> V *=0.017
<u> V *=0.025
<v> V *=0.025
<u> V *=0.033
<v> V *=0.033
0.4
0.2
0
0
0.2
0.4
0.6
u0=0.88 m/s
<u'2>1/2 V*=0
<v'2>1/2 V *=0
<u'2>1/2 V*=0.008
<v'2>1/2 V *=0.008
<u'2>1/2 V*=0.017
<v'2>1/2 V *=0.017
<u'2>1/2 V*=0.025
<v'2>1/2 V *=0.025
<u'2>1/2 V*=0.033
<v'2>1/2 V *=0.033
0.4
0.2
0.6
0.8
0
1
Velocity (m/s)
0
0.1
0.2
0.3
Fluctuation Velocity (m/s)
Fig. 2. (a) The ensemble velocity distributions and (b) the fluctuation velocity distributions in the
shear cell for the five different moisture cases.
The Jenike shear tester is used to measure the wall and internal friction coefficients. Fig. 3(a)
and (b) show the wall and internal friction coefficients plotted against the moisture content. It shows
that the internal friction coefficients are higher than the wall friction coefficients. The wall and
internal friction coefficients increase with increasing the moisture content. There is a cohesive force
between wet particles which leads to the granular flow more viscous (Yang and Hsiau, 2001;
Oulahna et al., 2003). Fig. 3(a) and (b) also remonstrate that the viscous forces existing between
wet particles result in the higher friction coefficients. The more viscous granular flow needs energy
to keep the flow system, because the input energy has to provide the energy dissipated through the
viscous effect. The above effect retards the flow causing the weaker movements in the system with
high moisture content.
The Jenike shear tester can also measure the cohesive force between particles. Fig. 3(c) shows
the cohesive force plotted against the moisture content. The cohesive force also increases with
increasing the moisture content. Fig. 3(c) indicates that the force of particles is greater in wetter
granular flow and influences the flowing behavior deeply.
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5th International Conference on Multiphase Flow, ICMF’04
Yokohama, Japan, May 30–June 4, 2004
Paper No. 308
0.65
(a)
wall Friction Coefficient
0.6
0.55
0.5
0.45
0.4
0
0.01
0.02
V*
0.03
0.04
0.7
Internal Friction Coefficient
(b)
0.65
0.6
0
0.01
0.02
V*
0.03
0.04
10
C ( x10 -3 kPa)
(c)
5
0
0
0.01
0.02
V*
0.03
0.04
Fig. 3. (a) The wall and (b) the internal friction coefficients and (c) the cohesive force versus the
moisture content.
Fig. 3(a) and (b) and (c) show that the moisture influences the flow properties of the granular
system. To examine the influences of the moisture contents on the shear rate (strain rate) and the
shear stress along the upper walls, there are five moisture contents (V* = 0, 0.008, 0.017, 0.025 and
0.033). Fig. 4 shows the normal stress yy and the shear stress xy on the upper walls plotted against
the shear rate for the five tests. In our earlier researches (Hsiau and Yang, 2002; Hsiau and Yang,
2004), the slopes of the normal and shear stresses both are the square of the shear rates. However,
the slopes of the normal and shear stresses in this paper are 2.506 and 0.845. Because the square
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Paper No. 308
power relations between the stresses and the shear rates are for the dry granular flows. In this study,
the particles in granular flows are wet with significant cohesive effect. The power relations between
the stresses and the shear rates are not square, but remain as positive. Fig. 4 also indicates that the
granular flows have smaller shear rates and smaller normal and shear stresses. It indicates that there
are greater cohesive forces between the wetter granular system.
25
Stress (kPa)
20
u0=0.88 m/s
V* = 0
V* = 0.008
V* = 0.017
V* = 0.025
V* = 0.033
15
Normal Stress
10
5
0
45
Shear Stress
50
55
60
Shear Rate (1/s)
Fig. 4. The normal and shear stresses as functions of the shear rate.
According the ratio of velocity between streamwise flow in every region and the bottom disk,
we distinguish three regions from test region. (1) “Uniform region” is that when the directional
velocity of streamwise flow is greater than 95% velocity of the bottom disk. (2) “Low shear region”
is that when the velocity of streamwise flow than bottom disk is between 85% and 95%. (3) “High
shear region” is that when the directional velocity of streamwise flow is lower than 85% velocity of
the bottom disk. Another important transport property is the self-diffusion coefficient, which uses
the experiment method of Hsiau and Shieh (1999) and computes the historical trace of mean-square
diffusive displacements in the direction of <xx> and <yy>. Fig. 5 means the mean-square
streamwise and transverse diffusive displacements varied with time in three flow regions for the
moisture content V* of 0.008, when we control the input energy be a constant. The velocity of
bottom disk is measured at 0.88 m/s. We need to deduct the mean-square diffusive displacements,
which are caused by whole flow field from mean-square diffusive displacements in the direction of
<xx>. As equation (7) the mean-square diffusive displacements are linear increase with time in
the three regions of streamwise and transverse direction. In high shear region, the mean-square
diffusive displacements are greater. The mean-square diffusive displacements in transverse
direction are smaller than in streamwise direction.
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Paper No. 308
100
30
(a)
High Shear
Low Shear
Uniform
<y  y> (x10 -6 m2)
<x  x> ( x10 -6 m2)
80
(b)
v* = 0.008
u0 = 0.88 m/s
High Shear
Low Shear
Uniform
60
40
v* = 0.008
u0 = 0.88 m/s
20
10
20
0
0
0.5
0
1
0
0.5
Time (s)
1
Time (s)
Fig. 5. The mean-square (a) streamwise and (b) transverse diffusive displacements varied with time
in three flow regions for the moisture content V* of 0.008.
The self-diffusion coefficient can be determined from relation between mean-square diffusive
displacements, eq. (7). For the five different moisture contents with the bottom velocity of 0.88 m/s,
the self-diffusion coefficients in the streamwise direction Dxx and transverse direction Dyy at the
three flow regions were plotted against the channel height in Fig. 6 (a) and (b). The self-diffusion
coefficients in the streamwise direction are larger than in the transverse direction. The diffusion
coefficients are greater in the high shear region and the case with low moisture contents. The
deviation is not significant in the uniform region for the five tests. The diffusion coefficients mean a
disturbed status in the flow field, if the diffusion coefficients are small, and they mean the fluid of
flow field is inactive. According to Fig. 6 (a) and (b), if the moisture contents are larger, then
diffusion coefficients in the flow field are smaller. That’s matching with our former discussion and
verifying that in the granular flow with a little wet will become more viscous and flow behavior is
not smooth. Thus, the granular flow should keep the dry status and aid the granular transportation.
30
5
(b)
(a)
High Shear
High Shear
4
20
D yy ( x10 -6 m2/s)
D xx ( x10 -6 m2/s)
25
Low Shear
15
Uniform
u0=0.88 m/s
10
0
0
0.25
0.5
0.75
Low Shear
2
u0=0.88 m/s
Uniform
V *=0
V *=0.008
V *=0.017
V *=0.025
V *=0.033
5
3
V *=0
V *=0.008
V *=0.017
V *=0.025
V *=0.033
1
0
1
Scaled Height, y/h
0
0.25
0.5
0.75
1
Scaled Height, y/h
Fig. 6. The self-diffusion coefficients (a) in the streamwise direction and (b) in the transverse
direction at the three flow regions versus the channel height for the five tests with different moisture
contents.
In this study, we measure the Granular Bond Number Bog of 2.003256 is greater than 1. It
indicates that the particles in the current granular flow systems have cohesive effect. Fig. 7 (a) and
(b) present the relations between the streamwise and transverse self-diffusion coefficients and the
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Paper No. 308
Collision Number CO for five different granular moisture contents. The wetter granular flows have
greater values of the collision number. From eq. (6), the maximum cohesive force in this study is
constant. Therefore, the value of collision number increases with decreasing the collision force. The
wetter granular flows have greater cohesive forces lead to the lower shear rates. The collision forces
are positive relation to the shear rates. So the more wet granular flows have the greater values of the
collision number. In McCarthy’s research (2003), the dynamic formation/breakage of liquid bridges
results in a viscous force resisting motion, derived from lubrication theory. It is essential that any
liquid-induced cohesion model include these effects as they may become large relative to the
capillary force as the particle velocity increases (Ennis et al., 1990). The collision number in the
uniform region is greater than in the high shear region, because there is lower perturbation motion
in the uniform region.
30
5
(a)
High Shear
20
u0=0.88 m/s
V *=0
V *=0.008
V *=0.017
V *=0.025
V *=0.033
4
High Shear
D yy ( x10 -6 m2/s)
25
D xx ( x10 -6 m2/s)
(b)
u0=0.88 m/s
V *=0
V *=0.008
V *=0.017
V *=0.025
V *=0.033
15
10
3
2
Low Shear
Uniform
1
5
0
0
10
20
30
40
0
50
Co
Low Shear
0
10
Uniform
20
30
40
50
Co
Fig. 7. The variations of (a) the streamwise and (b) the transverse self-diffusion coefficients with
the collision number.
4.Conclusion
This paper is discussed about flow property of granular material in a two-dimension shear cell.
By using the image processing technology and particle tracking method we get the fluctuation
velocity and self-diffusion coefficient. Besides, using three bi-directional stress gages to measure
the normal and shear stresses on the upper wall with five different moisture granular flows and
using Jenike shear tester to measure the friction coefficient and cohesion with these different
moisture contents and study the influence of wet particle for flow property. In the test region exists
three flow regions that are uniform region, low shear region and high shear region. Using the figure
of mean-square diffusive displacements and time to get the self-diffusion coefficient and the
diffusion coefficient that is Dxx,and Dyy will increase with decreasing the collision number. The
self-diffusion coefficients and fluctuations in the streamwise direction are much higher than those in
the transverse direction and use the result of experiment in the different transport property to
compare with the assumption of dense-gas kinetic theory. From the experiments, the friction angle
and cohesive force of wet particles are larger than those of dry particles. However, for the wetter
granular material flows, the average and fluctuation velocities and the self-diffusion coefficients in
the streamwise and transverse directions are lower. It indicates that the wet granular flows have
greater viscous forces and liquid bridge force which results in the weaker dynamic behaviors. The
self-diffusion coefficients are increased with the increase of the velocity fluctuations, the shear rates
and the stresses.
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5th International Conference on Multiphase Flow, ICMF’04
Yokohama, Japan, May 30–June 4, 2004
Paper No. 308
Acknowledgements
Financial support from the National Science Council of the R.O.C. for this work through
projects NSC 91-2212-E-008-033 and NSC 92-2212-E-008-007 are gratefully acknowledged.
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