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Low‐Reynolds‐number flow between converging spheres
Author(s) -
Jeffrey D. J.
Publication year - 1982
Publication title -
mathematika
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.955
H-Index - 29
eISSN - 2041-7942
pISSN - 0025-5793
DOI - 10.1112/s002557930001216x
Subject(s) - spheres , reynolds number , mathematics , flow (mathematics) , reynolds equation , constant (computer programming) , lubrication theory , asymptotic expansion , mechanics , mathematical analysis , lubrication , geometry , physics , thermodynamics , turbulence , astronomy , computer science , programming language
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).