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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

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