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Low-Reynolds-number flow between converging spheres

Part of: Incompressible viscous fluids

Published online by Cambridge University Press:  26 February 2010

D. J. Jeffrey
D. J. Jeffrey
Affiliation:
Department of Applied Mathematics and Theoretical Physics, Silver Street, Cambridge. CB3 9EW.
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Abstract

Two spheres of different radii are approaching each other with equal and opposite velocities, the fluid flow around them being at low Reynolds number. The forces on the spheres can be calculated when they are very close by applying an asymptotic analysis — usually called lubrication theory — to the flow in the gap between the spheres. If the non-dimensional gap width is ε, the force is calculated here correct to O(ε In ε) for all ratios of the two spheres' radii. The analysis can be combined with earlier numerical calculations to find all the constants in the asymptotic expansion correct to O(ε).

MSC classification

Secondary: 76D10: Boundary-layer theory, separation and reattachment, higher-order effects
Type
Research Article
Information
Mathematika , Volume 29 , Issue 1 , June 1982 , pp. 58 - 66
Copyright
Copyright © University College London 1982

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References

Batchelor, G. K. and Wen, C.-S.. 1982. Sedimentation in a polydisperse system of interacting spherical particles. Part 2. Submitted to J. Fluid Mech.CrossRefGoogle Scholar
Brenner, H.. 1961. The slow motion of a sphere through a viscous fluid towards a plane surface. Chem. Eng. Sri., 16, 242–251.CrossRefGoogle Scholar
Cooley, M. D. A. and O'Neill, M. E.. 1969a. On the slow motion generated in a viscous fluid by the approach of a sphere to a plane wall or stationary sphere. Mathematika, 16, 37–49.CrossRefGoogle Scholar
Cooley, M. D. A. and O'Neill, M. E.. 1969b. On the slow motion of two spheres in contact along their line of centres through a viscous fluid. Proc. Camb. Phil. Soc, 66, 407–415.CrossRefGoogle Scholar
Hansford, R. E.. 1970. On converging solid spheres in a highly viscous fluid. Mathematika, 17, 250–254.CrossRefGoogle Scholar
Happel, J. and Brenner, H.. 1965. Low Reynolds Number Hydrodynamics. (Prentice-Hall).Google Scholar
Jeffrey, D. J.. 1978. The temperature field or electric potential around two almost touching spheres. J. Inst. Math. Appl., 22, 337–351.CrossRefGoogle Scholar
O'Neill, M. E. and Stewartson, K.. 1967. On the slow motion of a sphere parallel to a nearby plane wall. J. Fluid Mech., 27, 705–724.CrossRefGoogle Scholar