Squeeze Flow of a Power-Law Fluid Between Two Rigid Spheres With Wall Slip
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摘要: 基于Reynolds润滑理论分析了壁面滑移对任意圆球颗粒间幂律流体的挤压流动的影响。研究表明有壁面滑移时挤压流动的粘性力可通过引进本文定义的滑移修正系数分离出无滑移解。推导出的挤压力滑移修正系数是一积分表达式,依赖于滑移参数、幂律指数、球间隙和积分上限。一般地壁面滑移导致粘性力减小,粘性力的减小量随幂律指数的增大而增大,表明壁面滑移对剪切增稠流变材料有更大的影响;粘性力的减小量还随着滑移参数的增大而增加,而这恰与假设相符合;粘性力的减小量又随球间隙减小或积分上限的增大(从液桥情况到完全浸渍)而减小直到趋于常数,这一特性在离散元模拟时可以有效地减少计算量。Abstract: The effect of wall slip on the squeeze flow of a power-law fluid between two rigid spherical particles has been examined based on the Reynolds lubrication theory. It is shown that the viscous force arising from the squeeze flow with wall slip may be resolved to the no-slip solution by introducing a slip correction coefficient. An expression for the slip correction coefficient of force is derived which is related to the slip parameter, the flow index and the upper limit of integration. Generally, wall slip results in a reduction in the viscous force. The reduction in the viscous force increases as the flow index increases, suggesting that wall slip has a more profound effect on shear thickening material. However, such reduction decreases as the upper limit of integration increases from finite liquid bridges to fully immersed systems. The reduction in the viscous force also increases as the slip parameter increases, which is the expected behaviour.
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Key words:
- lubrication /
- power-law fluid /
- squeeze flow /
- viscous force /
- wall slip /
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[1] Bird R B,Armstrong R C,Hassager O.Dynamics of Polymeric Liquids[M].New York:Wiley,1977,19-21. [2] Scott J R.Theory and application of the parallel plate viscometer[J].Trans Ins Rubber Ind,1931,7(2):169-186. [3] Davis A M J,Frenkel A L.Cylindrical liquid bridges squeezed between parallel plates:exact Stokes flow solutions and hydrodynamic forces[J].Phys Fluids A,1992,4(6):1105-1109. [4] Laun H M,Rady M,Hassager O.Analytical solutions for squeeze flow with partial wallslip[J].Journal of Non-Newtonian Fluid Mechanics,1999,81(1-2):1-15. [5] Adams M J,Edmondson B.Forces between particles in continuous and discrete liquid media[A].In:B J Briscoe,M J Adams Eds.Tribology in Particulate Technology[C].1987,154-172. [6] Rodin G J.Squeeze film between two spheres in a power-law fluid[J].Journal of Non-Newtonian Fluid Mechanics,1996,63(2-3):141-152. [7] Xu Y,Huang W,Lian G.On the normal viscous force between two colliding spheres with an interstitial power-lawliquid[A].In:Kishino Ed.Pow ders & Grains 2001(4th International Conference on Micromechanics of Granular Media)[C].Lisse:Swets & Zeitlinger,2001,611-614. [8] Lian G,Xu Y,Huang W,et al.On the squeeze flow of power-law fluid between rigid spheres[J].Journal of Non-Newtonian Fluid Mechanics,2001,100(2-3):151-164. [9] Mooney M.Explicit formulae for slip and fluidity[J].Journal of Rheology,1931,2(2):210-222. [10] Atwood B T,Schowalter W R.Measurement of slip at the wall during the flow of high density polyethylene through a rectangular conduit[J].Rheol Acta,1989,28(2):134-146. [11] Kraynik A M,Schowalter W R.Slip at the wall and extrudate rough ness with aqueous solutions of polyvinyl alcohol and sodium borate[J].Journal of Rheology,1981,25(1):95-114. [12] Ramamurthy A V.Wall slip in viscous fluids and influence of material construction[J].Journal of Rheology,1986,30(2):337-357. [13] Melrose J R,Van Vliet J H,Ball R C.Continuous shear thickening and colloid surfaces[J].Physics Review Letter,1996,77(22):4660-4663. [14] Lian G,Thornton C,Adams M J.Discrete particle simulation of agglomerate impact coalescence[J].Chem Engng Sci,1998,53(19):3381-3391. [15] Rao I J,Rajagopal K R.The effect of slip boundary condition on the flow of fluids in a channel[J].Acta Mechanica,1999,135(1-2):113-126. [16] Joshi Y M,Lele A K,Mashelkar R A.A unified wall slip model[J].Journal of Non-Newtonian Fluid Mechanics,2000,94(2-3):135-149. [17] Cohen Y,Metzner A B.Apparent slip flow of polymer solutions[J].Journal of Rheology,1985,29(1):67-102.
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