SQUEEZE FLOW OF A POWER-LAW FLUID BETWEEN TWO RIGID SPHERES WITH WALL SLIP

Applied Mathematics and Mechanics (English Edition) ›› 2002, Vol. 23 ›› Issue (7): 811-818.

SQUEEZE FLOW OF A POWER-LAW FLUID BETWEEN TWO RIGID SPHERES WITH WALL SLIP

黄文彬¹, 徐泳¹, 练国平², 李红艳¹

1. Department of Engineering Sciences, China Agricultural University, Beijing 100083, P R China;
2. Unilever Research Colworth Laboratory, Sharnbrook, Bedford MK44 1LQ, UK

收稿日期:2001-10-09 修回日期:2002-03-28 出版日期:2002-07-18 发布日期:2002-07-18
基金资助:
the National Natural Science Foundation of China(19972075);Unilever Plc

SQUEEZE FLOW OF A POWER-LAW FLUID BETWEEN TWO RIGID SPHERES WITH WALL SLIP

HUANG Wen-bin¹, XU Yong¹, LIAN Guo-ping², LI Hong-yan¹

1. Department of Engineering Sciences, China Agricultural University, Beijing 100083, P R China;
2. Unilever Research Colworth Laboratory, Sharnbrook, Bedford MK44 1LQ, UK

Received:2001-10-09 Revised:2002-03-28 Online:2002-07-18 Published:2002-07-18
Supported by:
the National Natural Science Foundation of China(19972075);Unilever Plc

摘要/Abstract

摘要： 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.

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.

中图分类号:

O347.7
O373

黄文彬;徐泳;练国平;李红艳. SQUEEZE FLOW OF A POWER-LAW FLUID BETWEEN TWO RIGID SPHERES WITH WALL SLIP[J]. Applied Mathematics and Mechanics (English Edition), 2002, 23(7): 811-818.

HUANG Wen-bin;XU Yong;LIAN Guo-ping;LI Hong-yan. SQUEEZE FLOW OF A POWER-LAW FLUID BETWEEN TWO RIGID SPHERES WITH WALL SLIP[J]. Applied Mathematics and Mechanics (English Edition), 2002, 23(7): 811-818.

参考文献

[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 vi scometer[J]. Trans Ins Rubber Ind,1931,7(2):169-186.
[3] Davis A M J, Frenkel A L. Cylindrical liquid bridges squee zed betw een 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 squ eeze flo w with partial wall slip[J]. Journal of Non-Newtonian Fluid Mechanics,1999,81(1-2):1-15.
[5] Adams M J, Edmondson B. Forces between particles in contin uous and discrete liquid media[A]. In: B J Briscoe, M J Adams Eds. Tribology in Part iculate 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 col liding spheres with an interstitial power-law liquid[A]. In: Kishino Ed. Pow ders & Grains 2001(4th International Conference on Micromechanics of Granular Me dia)[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 durin g the flow of high density polyethylene through a rectangular conduit[J]. Rh eol 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]. Journ al of Rheology,1981,25(1):95-114.
[12] Ramamurthy A V. Wall slip in viscous fluids and influence of mate rial 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 ag glomerate 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):1 35-149.
[17] Cohen Y, Metzner A B. Apparent slip flow of polymer solutions[J]. Journal of Rheology,1985,29(1):67-102.

SQUEEZE FLOW OF A POWER-LAW FLUID BETWEEN TWO RIGID SPHERES WITH WALL SLIP

SQUEEZE FLOW OF A POWER-LAW FLUID BETWEEN TWO RIGID SPHERES WITH WALL SLIP

PDF

可视化

摘要/Abstract

引用本文

使用本文

参考文献

相关文章 1

编辑推荐

Metrics

本文评价