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On the slow viscous rolling of a sphere in contact with a permeable surface
Author(s) -
Nir Avinoam
Publication year - 1980
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/s0025579300009992
Subject(s) - conformal map , mathematics , permeability (electromagnetism) , mechanics , surface (topology) , porosity , mathematical analysis , classical mechanics , divergence (linguistics) , boundary value problem , porous medium , geometry , physics , materials science , chemistry , composite material , linguistics , philosophy , biochemistry , membrane
An exact solution for the velocity field induced by the slow rolling motion of a sphere in contact with a permeable surface is derived. The porous solid and the viscous fluid each occupies a semi‐infinite space. It is shown that, by the use of conformal mapping, the problem is reduced to a fourth order ordinary linear boundary value problem. As the permeability of the porous body diminishes the important functionals, e.g . the force and torque resisting the rolling motion of the sphere, are divergent. The nature of this divergence is found and the dependence on the permeability of the porous solid is explicitly evaluated.