Powder Technology 270 (2015) 348–357

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Bottom wall friction coefficients on the dynamic properties of shearedgranular flows

Chun-Chung Liao, Shu-San Hsiau ⁎, Pei-Sian ChangDepartment of Mechanical Engineering, National Central University, Jhongli 32001, Taiwan, ROC

⁎ Corresponding author at: No. 300, Jhongda Rd., JhongTaiwan. Tel.: +886 3 426 7341; fax: +886 3 425 4501.

E-mail address: sshsiau@cc.ncu.edu.tw (S.-S. Hsiau).

http://dx.doi.org/10.1016/j.powtec.2014.10.0430032-5910/© 2014 Elsevier B.V. All rights reserved.

a b s t r a c t

a r t i c l e i n f o

Article history:Received 17 February 2014Received in revised form 23 October 2014Accepted 26 October 2014Available online 31 October 2014

Keywords:Sheared granular flowsBottom wall friction coefficientTangential velocityGranular temperature

In this study, we used a two-dimensional annular shear cell to systematically investigate the dynamic propertiesof granular flowwhen it is subjected to varying bottomwall friction coefficients. A particle trackingmethod andimage processing technologywere employed tomeasure tangential velocity, slip velocity, local solid fraction, andgranular temperature. The results demonstrated that the bottom wall friction coefficient played a crucial role indetermining the dynamic properties of sheared granular flows, indicating that slip velocity is larger when arougher bottom wall is applied. The results also indicated that the tangential velocity and granular temperaturewere reduced when the roughness of the bottom wall increased because of the strong frictional effect, whichcaused a larger dissipation of energy. The average granular temperature increased linearlywhen the solid fractionat each specific bottom wall friction coefficient increased.

© 2014 Elsevier B.V. All rights reserved.

1. Introduction

Granular materials are found in many industrial processes, such as incoal transportation, pharmaceutical manufacturing, food storage andtransport, polymer production, pyrolysis of biomass, and metallurgicalengineering, as well as in daily life, such as in sand, salt, sugar, andbeans. The handling and processing of granularmaterials are of economicimportance in many industries. Furthermore, to predict and prevent di-sasters caused by uncontrolled debris flows, avalanches, and landslides,it is crucial to understand the dynamic properties and rheology of thesephenomena. However, the present understanding of the behavior ofgranular flows remains inadequate and a deeper study is necessary.

Granular materials do not flow homogeneously like a fluid becausethe external driven force does not exceed a critical value and energy dis-sipation resulting from the occurrence of inelastic collisions, as well asfrom friction between particles and between particles and walls. There-fore, a solid-like region and a liquid-like region (shear band region) cancoexist in the same flow system. The thickness of a shear band is ap-proximately four to ten particle diameters, which depends on the exter-nal driving conditions, solid fraction, and interstitial fluid viscosity[1–5]. The interactive collisions that occur between particles cause therandommotions of these particles, which become the dominant mech-anism influencing flow behavior in granular materials [6,7]. Randomparticlemotion in granularflows is analogous to thermalmolecularmo-tion. The concept of granular temperature was first proposed by Ogawa[8] to quantify themean-square value of fluctuation velocities. Granular

li City, Taoyuan County 32001,

temperature is defined as the specificfluctuation in the kinetic energy ofparticles that are present in granularflows, and it plays a role in granularflows that is similar to that of thermodynamic temperature in a gas.Granular materials behave more like a liquid or a gas when they havea higher granular temperature.

In the past few decades, shear cells have beenwidely used for inves-tigating the dynamic properties and rheology of granular materials be-cause they exhibit a relatively simple flow field, which makes themsuitable for fundamental research [9–24]. According to the Reynoldsshear dilatancy phenomenon, the packing structure of granular matterbecomes diluted as a shear force is applied [25]. Mahmood et al. [17] in-vestigated the micromechanics of granular flows by using a two-dimensional planar granular Couette flow. They determined that fluctu-ation velocity and granular temperature are related to the effectiveshear rate. They also indicated that the distribution of collision anglesis anisotropic. Koval et al. [18] studied sheared granular flow by usinga discrete element simulation in which an effective wall velocity wasused to generate an inertia regime (shear band) near the rotatinginner wall, whereas away from thewall a quasi-static regime prevailed,in which the granular material was in a solid or near-solid phase andparticle motions were correspondingly slow and weak.

The wall friction effect exerts a significant influence on dynamicproperties and flowbehaviors in granularflows. Hsiau and Yang [15] in-dicated that the rougher the condition of a wall, the greater the stressthat is induced, and the higher the shear rate in sheared granularflows. Jasti and Higgs [21] experimentally studied granular flows in anannular shear cell and observed that particle velocity and granular tem-perature increased with increasing shearing wall roughness. Marinacket al. [26] used different shearing wall surface materials to produce dif-ferent coefficients of restitution between the granular and shearing

Bottom wall

Fig. 1. Schematic drawing of (a) the shear cell experimental apparatus; (b) side view of the shear cell.

Table 1Parameters used in the current experiments.

Bottom wall friction coefficient (μw) Inner wallvelocity Ui (m/s)

Area solidfraction (v)

0.384 (#220 (68 μm) sandpaper) 0.23 m/s 0.820.378 (#240 (61 μm) sandpaper) 0.34 m/s0.354 (#280 (51 μm) sandpaper) 0.45 m/s0.316 (#320 (45 μm) sandpaper) 0.57 m/s0.300 (#400 (38 μm) sandpaper) 0.68 m/s

1.02 m/s0.384 (#220 (68 μm) sandpaper) 1.02 m/s 0.780.378 (#240 (61 μm) sandpaper) 0.800.354 (#280 (51 μm) sandpaper) 0.820.316 (#320 (45 μm) sandpaper) 0.840.300 (#400 (38 μm) sandpaper)

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surfacematerialswith the same shearingwall roughness and found thatthe velocity and granular temperature increased with the increase ofrestitution coefficient. Hsiau et al. [19] observed that convection andsegregation rates increased with an increasing side wall friction coeffi-cient in a vertical vibration bed. Kose et al. [22] experimentally investi-gated the rheology of particle–liquid mixtures by using both smoothand rough wall surfaces in sheared granular flows. They observed thatthe effective mixture viscosity is larger in cases involving rougher wallsurfaces than in cases involving smoother wall surfaces. They demon-strated that wall slip substantially affects the apparent viscosity.

In the past, the effect of driving wall roughness on dynamic proper-ties had received a lot of attention. The influence of bottomwall rough-ness on the dynamic properties in sheared granular flows has not beenpreviously examined. Additionally, the bottom surface is usually unevenin most industrial and natural granular systems. Hence, it is importantto study the effect of bottom wall friction coefficient on dynamic

350 C.-C. Liao et al. / Powder Technology 270 (2015) 348–357

properties in sheared granular flows. In the present study, the effects ofvarious bottom wall friction coefficients on the dynamic properties ofsheared granular materials were investigated. The tangential velocities,slip velocities, local solid fractions, and granular temperatures were de-termined and discussed.

2. Experimental setup

A schematic drawing of a two-dimensional annular shear cell isshown in Fig. 1(a). The inner driving wall has a radius, ri, of 105 mm,and the distance from the center of the inner wheel to the rim of the

Fig. 2. Distributions of tangential velocities with radial position for different wall velocities, (a)area solid fraction v = 0.82.

outer driving wheel, ro, is 150 mm (Fig. 1(b)). In this study, the radialposition was normalized as (r–ri)/(ro–ri) from 0 (inner wall boundary)to 1 (outer wall boundary), with r being the distance from the centerof the innerwheel. The inner and outer walls were driven independent-ly by two server motors. The width of the annular trough between theinner wheel and the rim of the outer wheel was 45 mm. The granularmaterials were placed on the annular trough for testing. The rotationalspeeds of the inner and outer walls were measured individually byusing a tachometer, and the velocities, Ui for the inner wheel and U0

for the outer wheel, were calculated as a product of the rotationalspeed and radius of the wall. In this study, the inner wall velocity was

μw = 0.384; (b) μw = 0.378; (c) μw = 0.354; (d) μw = 0.316; (e) μw = 0.300 at a specific

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varied and the outer wall was fixed in a stationary position to investi-gate the effect of the bottom wall friction coefficient on the dynamicproperties of sheared granular flows. The top surface of the apparatuswas fabricated using transparent glass to allow visual observation andreduce electrostatic buildup. Five different bottom wall surface condi-tions were used in this study: #220 sandpaper, #240 sandpaper, #280sandpaper, #320 sandpaper, and #400 sandpaper were glued to thebottom wall surface. The friction coefficients of 3.0 mm glass beadsand the five bottom wall surface conditions were measured using acommercial Jenike shear tester with direct shear model: 0.384 (#220sandpaper), 0.378 (#240 sandpaper), 0.354 (#280 sandpaper), 0.316(#320 sandpaper), and 0.300 (#400 sandpaper). By altering the rota-tional speed of the inner wall and the area solid fractions accordingly,the effect of the bottom wall friction coefficient on the dynamic

Fig. 3. Distributions of tangential velocities with radial position for different area solid frac(c) μw = 0.354; (d) μw = 0.316; (e) μw = 0.300.

properties of sheared granular flows was investigated. The detailedexperimental parameters are listed in Table 1.

Mono-sized glass beads with a diameter of 3 mm, a standard devia-tion of 0.09 mm, and a density of ρp = 2.476 g/cm3 were used as thegranular materials in this study. In this study, the internal friction coef-ficient of 3 mm glass beads was also measured by a commercial Jenikeshear tester with direct shear model and the value is 0.54. Additionally,the restitution coefficient of the glass bead used in this study, measuredby the drop test is 0.90. The kinetic energy of particles was dissipateddue to the inelastic collisions and friction effect. Only one layer ofbeads was placed in the container to enable the two-dimensional treat-ment of the granular system. The particles are in continuous contactwith the bottom wall in this study. The average area solid fraction, ν,was defined as v = Ap / As, where Ap was the cross-sectional area of

tions at a specific inner wall velocity, Ui = 1.02 m/s, (a) μw = 0.384; (b) μw = 0.378;

Fig. 4. Average tangential velocity plotted as a function of the area solid fraction with dif-ferent bottomwall friction coefficients μw, at the same inner wall velocity, Ui = 1.02 m/s.The error bars correspond to the standard deviation of at least three experimental tests ineach case.

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the particles that occupied the shear cell, as can be seen from the topview, and As was the entire area of the shear cell base [5]. To generatesufficient shear in the flow field, a layer of 3-mm glass beads wasglued to the surfaces of the inner and outer walls. A high-speed CCDcamera (IDT X-3 plus) was fixed above the shear cell to record the mo-tions of the beads, as shown in Fig. 1(a). A capture speed of 500 FPS andwith a resolution of 1200 × 400 pixels was used, and all images weretaken after the system had been shearing for at least 1 min to ensure asteady state of the flow field. The particle tracking velocimetry tech-nique was used to calculate the velocity of the beads by locating theircenters in the high-speed images and determining their displacementsbetween two consecutive images [5,14,27].

The test section was radially divided into 10 regions. The localarea solid fraction in each radial region can be determined as followsvi = Api / Asi, where Api was the cross-sectional area of the particlesthat occupied the radial region i and Asiwas the area of the radial regioni [5,21,26]. The ensemble averages of the tangential bVθN and radial bVrNvelocities in each radial region were obtained from approximately 1200particles, as follows:

bVθN ¼

XN

k¼1

Vθ;k

N; ð1Þ

bVrN ¼

XNk¼1

Vr;k

N; ð2Þ

where k represents the kth particle, N is the total number of velocitiesused for averaging the mean values, and Vθ,k and Vr,k are the velocitiesof the kth particle measured from two consecutive images containingthe kth particle. The fluctuation velocities in the two directions weredetermined as follows:

bVθ

0 2N1=2 ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiXN

k¼1

Vθ;k−bVθN� �2

N−1

vuuuut; ð3Þ

bVr

0 2N1=2 ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiXN

k¼1

Vr;k−bVrN� �2

N−1

vuuuut: ð4Þ

The granular temperature, T, was used to quantify the kinetic energyof the granular flow and was calculated from the average of the meansquare of the fluctuation velocities in both directions. The granular tem-perature in a quasi-two-dimensional system was calculated as

T ¼ bVθ

0 2 þ Vr

0 2N

2: ð5Þ

In this study, only one layer of particles was used, therefore everyparticlewas always in contactwith the solid bottomwall of the contain-er. When the granularmaterials were sheared to flow, the granularma-terials interacted continuously with the solid bottom wall of thecontainer. Naturally, friction occurred between the container wallsand particles, and this, aswell as the inelastic collisions and internal fric-tion between the particles themselves, meant that the kinetic energy ofthe particles was continuously dissipated. Therefore, external energyhad to be constantly introduced into the granular system to maintainthe granular temperature.

The slip velocity at the driving wall was determined using the fol-lowing equation based on previous studies [5,21,26]:

S ¼ Ui−Vθ;1; ð6Þ

where Ui was the tangential velocity of the inner wall and Vθ,1 was theaverage tangential velocity of the bin adjacent to the boundary of thedriving inner wall. It is noted that the particles of the bin adjacent tothe boundary of the driving inner wall are in contact with the drivinginner wall. In this study, each case was repeated at least three timesto calculate the average tangential velocity and average granulartemperature.

3. Results and discussion

Fig. 2(a) shows the distributions of the tangential velocities acrossthe normalized radial position, (r–ri)/(ro–ri), with r being the distancefrom the center of the inner wheel for different inner wall velocities,Ui, at a specific bottom wall friction coefficient, μw = 0.384, and solidfraction, v = 0.82. The velocity profile illustrates that these velocitiesdecreased gradually from the shearing boundary to the stationarywall. The velocity gradient was larger near the driving wall because ofthe higher shear rate. Additionally, this velocity profile illustrates thatthe velocity gradient became larger with the higher wall velocity,which caused stronger particle motions. Interactive inelastic collisionsoccurred in areas that were closer to the driving wall boundary, andgrew weaker the further they were from the driving wall. The particlesthat were close to the driving wall behaved like a fluid and constitutedthe region known as the shear band [3–5,10]. The behavior of the gran-ular flow in the shear band was primarily influenced by the interactiveinelastic collisions that were occurring when a dynamic state wasachieved. When they were further away from the driving wall, the par-ticles received less kinetic energy, and the dominant mechanisminfluencing granular flow behavior became the sliding and rolling con-tact that is characteristic of a quasi-static state. Thus, the dense granularpacking and solid-like behavior of the granular material were observedclose to the stationary wall; this area is known as the solid-like or fric-tional region [4,5,21]. Fig. 2(b)–(e) displays the distribution of tangen-tial velocities across various radial positions, specifically regarding thevarious innerwall velocities thatwere acting at a specific area solid frac-tion of v = 0.82, with the varying bottom wall friction coefficients ofμw = 0.378, 0.354, 0.316, and 0.300. As previously explained, theshear band, with its higher velocity gradient, was observed close tothe driving inner wall in each case. From Fig. 2(a)–(e) the shear bandthickness is similar with different inner wall velocities and bottomwall friction coefficients at the specific solid fraction. However, thegreater bottom wall friction coefficient causes the smaller velocity gra-dient. Additionally, the velocity gradientwas enhancedwith an increase

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of driving wall velocity in each specific bottom wall friction coefficientcondition. The results also show that the tangential particle velocityconsiderably increased as the bottomwall friction coefficient decreased.The frictional effect is stronger as the larger bottom wall friction coeffi-cient was applied. Higher dissipation of kinetic energy from particleswould result in the smaller velocity gradient and tangential particlevelocity.

Fig. 3(a)–(e) shows the variations in tangential velocity across vari-ous radial positions for various area solid fractions, and atwall velocitiesof Ui =1.02 m/s, U0 = 0, with varying bottomwall friction coefficients,

Fig. 5.Distributions of local solid fraction with radial position for different area solid fractions a0.354; (d) μw = 0.316; (e) μw = 0.300.

which were (a) μw = 0.384; (b) μw = 0.378; (c) μw = 0.354;(d) μw = 0.316; and (e) μw = 0.300. The velocity profile was similarto that shown in Fig. 2. A shear band that exhibited strong particle mo-tions and interactive collisions near the driving wall boundary was ob-served in each case. This figure also demonstrates that the tangentialvelocity was greater at a higher solid fraction. The frequency of the in-elastic collisions that occurred between the particles and the drivingwall boundary were substantially higher in the systems that containedhigher solid fractions. As a result of these contacts between the particlesand the driving wall, the particles obtained kinetic energy from the

t a specific inner wall velocity, Ui= 1.02m/s, (a) μw= 0.384; (b) μw= 0.378; (c) μw=

Fig. 6. Slip velocity plotted as a function of inner wall velocity with different bottom wallfriction coefficients. The lines indicate the linear fits to the data.

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driving wall, which led to their motions being strengthened and theflow field becoming more active, which led to a greater tangential ve-locity. Again, Fig. 3(a)–(e) shows that the shear band thickness is simi-lar with different solid fractions and bottom wall friction coefficients atthe specific inner wall velocity. The smaller bottom wall friction coeffi-cient causes the greater velocity gradient.

Fig. 4 displays the average tangential velocity, which was plotted ona graph as a function of the area solid fraction with various bottomwallfriction coefficients at a specific inner wall velocity (Ui=1.02m/s,U0=0). The average tangential velocity was greater at the smaller bottomwall friction coefficient, and the variation of the average tangential ve-locity of the various bottom wall frictions increased with the area solidfraction. The frictional effect between the particles and the bottomwall was enhanced when the larger bottom wall friction coefficientwas applied. Consequently, a larger amount of the kinetic energy ofthe particleswas dissipated because of the serious frictional sliding con-tacts that occurred between the particles and the bottom wall, whichcaused a smaller velocity gradient and average tangential velocity. Re-garding the larger solid fraction, the granular packing was denser,which caused a higher collision frequency between the particles andthe driving wall. Therefore, the particles had larger kinetic energy andleaded to the serious frictional interactions between the particles andthe bottomwall surface. Consequently, the variance of the average tan-gential velocity at various bottomwall friction coefficients became larg-erwith the increase of the solid fraction. This phenomenon has not beendiscussed in previous studies. The result indicated that the average tan-gential velocity increased in conjunctionwith the area solid fraction at aspecific bottom wall friction coefficient. The result is in agreement withthe previous study [13]. Accordingly, it could be inferred that a greatersolid fraction caused a higher inelastic collision frequency between theparticles and the driving wall at the same wall velocity [5]. As men-tioned, the particles acquired kinetic energy from the driving wall,which strengthened their motions and enhanced the fluidization ofthe flow field, and caused a higher average tangential velocity. The re-sults can be explained from the distribution of the local solid fraction(as shown in Fig. 5) at wall velocities of Ui = 1.02 m/s, U0 = 0 with:(a) μw = 0.384; (b) μw = 0.378; (c) μw = 0.354; (d) μw = 0.316; and(e) μw = 0.300. These graphs show the distributions of local solid frac-tions with the radial position for various area solid fractions at a con-stant wall velocity. The local solid fraction was small when it wasclose to the driving wall because of the shear dilation effect. However,it grew larger with increased distance from the driving wall becausethe lower shear rates caused weaker particle motions. The local solidfraction became smaller as a smaller solid fraction was applied to thesystem, consistent with the findings of Liao et al. [5] and Jasti andHiggs [21]. Additionally, the local solid fraction in the shear band waslarger when the solid fraction was increased in each bottomwall frictioncoefficient case. Thus, the average tangential velocity was larger whenthere was an increase of the higher local solid fraction, which caused afaster frequency of interactive collisions, and a largermomentum transferbetween the particles and the driving wall boundary, as shown in Fig. 4.

Because of the existence of a slip velocity between the driving wallboundary and the particles near the drivingwall boundary, the externaldriving energy was not fully introduced into the granular system. It wascrucial to determine the slip velocity to quantify the external energythat was introduced into the granular system. Fig. 6 shows the slip ve-locity plotted as a function of the inner wall velocity, using varying bot-tom wall friction coefficients at a specific area solid fraction. The resultindicated that the slip velocity increased linearly in conjunction withthe inner wall velocity. These results were in good agreement withthose obtained in previous studies [5,21]. The slip velocity was shownto be greater at a greater bottom wall friction coefficient at any giveninnerwall velocity. A larger amount of the kinetic energy of the particleswas dissipated because of the stronger frictional effect that occurred be-tween the particles and the bottom wall, which caused a larger slip ve-locity when there was a greater bottomwall friction coefficient present.

Granular temperature is critical to the study of theflowbehaviors anddynamic properties of granular materials [5–8,15,21]. Fig. 7(a)–(e)shows the distributions of the granular temperature across the radial po-sition at various driving inner wall velocities with varying bottom wallfriction coefficients at v = 0.82. The local granular temperature couldbe regarded as the local specific kinetic energy in this study. It was ob-served that granular temperature was increased when the driving wallvelocity was higher at each bottom wall friction coefficient. A largeramount of energy was introduced to the granular system at the higherdriving wall velocity, which led to a more active fluid field, stronger par-ticlefluctuations, and increased granular temperature. The granular tem-perature was also observed to be higher close to the driving inner wall(in the shear band region). Kinetic energy was transmitted mainlythrough interactive inelastic collisions that occurred between particlesthat comprised the granular materials. The strength of the motions ofthe particles and interactive collisions was enhanced, causing additionalparticle fluctuations caused by the higher velocity gradient in the shearband region. Thus, the granular temperature was greater closer to thedrivingwall boundary. This was consistent with previous studies that in-dicated that granular temperature is produced by the velocity gradient[5,7]. As the distance from the driving wall increased, the lower shearrate (smaller velocity gradient) caused weaker fluctuations of the parti-cles (in the solid-like region), leading to a decrease in the granular tem-perature. The results were in agreement with those of previous studies[5,21].

Marinack et al. [26] reported that the normalized translational kinet-ic energy increased with the increase of global solid fraction. However,they didn't investigate the effect of bottom wall friction coefficient ongranular temperature (kinetic energy). It is important to study the effectof bottom wall friction coefficient on dynamic properties in shearedgranular flows because the bottom surface is usually uneven inmost in-dustrial and natural granular systems. In this study, we focus on the ef-fect of bottom wall friction coefficients on the dynamic properties insheared granular flows. To quantify the influence of the bottom wallfriction effect on the granular temperature in sheared granular flows,the average granular temperatures, which were averaged from thelocal granular temperatures in the 10 regions, were plotted as a functionof the solid fraction for various bottom wall friction coefficients at aspecific inner wall velocity, as shown in Fig. 8. The average granulartemperature decreased when the bottom wall friction coefficient in-creased in each specific area solid fraction. A larger amount of kineticenergy from theparticleswas dissipated and caused the smaller averagegranular temperature because of the stronger frictional effect that oc-curred when there was a larger bottom wall friction coefficient. The re-sults are not similar to most previous studies, where the granular

355C.-C. Liao et al. / Powder Technology 270 (2015) 348–357

temperature was strengthened with the greater shearing wall frictioncoefficient [15,21]. Based on the experimental results, the influence ofwall friction on the dynamic properties of granular flows is not the

Fig. 7. Distributions of granular temperature with the radial position for different wall velocitispecific area solid fraction v = 0.82.

same but depends on the granular system. As shown in Fig. 8, the aver-age granular temperature increased linearly with the solid fraction ineach specific bottom wall friction coefficient increased. The slopes

es, (a) μw = 0.384; (b) μw = 0.378; (c) μw = 0.354; (d) μw = 0.316; (e) μw = 0.300, at a

Fig. 8. Average granular temperature plotted as a function of the area solid fractionwith different bottom wall friction coefficients μw, at a specific inner wall velocity,Ui = 1.02 m/s. The lines indicate the linear fits to the data. The error bars correspond tothe standard deviation of at least three experimental tests in each case.

356 C.-C. Liao et al. / Powder Technology 270 (2015) 348–357

were 4.94 × 10−2, 2.93 × 10−2, 2.03 × 10−2, 1.62 × 10−2, and 1.72× 10−2, which correspond to the cases where μw = 0.300, 0.316,0.354, 0.378, and 0.384, respectively. Liao et al. [5] found that velocitygradient is the predominant parameter influencing the granular tem-perature. From Fig. 3(a)–(e), the shear band thickness is similar withdifferent solid fractions at the specific inner wall velocity and bottomwall friction coefficient. However, the velocity gradient is larger withthe higher solid fraction. The larger velocity gradient leads to the stron-ger particle fluctuations and the greater average granular temperature.Therefore, the average granular temperature became larger when thehigher the solid fraction was applied. Fig. 8 indicates that the variationof the average granular temperature at various bottom wall friction co-efficients became larger as a higher solid fraction was applied. The fric-tional interactions between the particles and the bottom wall werestrengthened with the increase of solid fraction. Thus, the variation be-tween average granular temperatures with different bottom wall fric-tion coefficients increased with the increase of the solid fraction, asshown in Fig. 8. Fig. 9 shows average granular temperature plotted asaverage tangential velocity with the same data as shown in Figs. 4 and8. The data are collapse and shows that average granular temperatureis enhanced with the increasing average tangential velocity.

Average tangential velocity (m/s)

Ave

rage

gran

ular

tem

pera

ture

(m2 /s

2 )

0.005 0.01 0.015 0.02 0.025 0.03

0.003

0.004

0.005

0.006

0.007

0.008

0.009

0.01

µw = 0.384µw = 0.378µw = 0.354µw = 0.316µw = 0.300

Fig. 9. Average granular temperature plotted as average tangential velocity with the samedata as shown in Figs. 4 and 8.

4. Conclusion

This study investigated the effects of bottomwall friction coefficientson the dynamic properties of two-dimensional sheared granular flows.The experiments were conducted at a two-dimensional annular shearcell. The particle tracking velocimetry technique and image processingtechnology were used to successfully determine the tangential velocity,slip velocity, granular temperature, and local solid fraction. The resultsrevealed that the bottomwall friction coefficient exerted a critical influ-ence on the dynamic properties of sheared granular flows, a phenome-non that has not previously been reported. The dynamic propertieswere mitigated with the rough bottom wall. Additionally, the resultsshowed that the slip velocity increased when a greater bottom wallfriction coefficient was applied. The average granular temperature in-creased linearly with the solid fraction and decreased when the bottomwall friction coefficient increased because of the strong frictional effect,which caused the smaller velocity gradient and a large dissipation of en-ergy. Furthermore, the variation in the average granular temperaturewhen different bottom wall friction coefficients were applied becamelarger with the higher solid fraction because of the severe frictionaleffect between the particles and the bottom wall. This study demon-strated that the bottom wall roughness impacts the flow differentlythan shearing wall roughness and decreased the dynamic propertieswithin the sheared granular system. A further study with differentsystems is required to clarify this wall friction effect.

Acknowledgments

The authors would like to acknowledge the support of the NationalScience Council Taiwan for this work through grant NSC 100-2221-E-008-078-MY3.

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