Asymmetric three-dimensional Stokes flows about two fused equal spheres

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Abstract

Exact solutions to three-dimensional Stokes flow problems for asymmetric translation and rotation of two fused rigid spheres of equal size have been obtained in toroidal coordinates. The problems have been reduced to three-contour equations for meromorphic functions from a certain class, and then the latter have been reduced to Fredholm integral equations of the second kind by the Mehler-Fock transform of order 1. For the specified class of functions, the equivalence of the corresponding three-contour and Fredholm equations has been established in the framework of Riemann boundary-value problems for analytic functions. As an illustration for the obtained solutions, the pressure has been calculated at the surface of the body for both problems, and resisting force and torque, experienced by the body in asymmetric translation and rotation, have been computed as functions of a geometrical parameter of the body.

Original languageEnglish
Pages (from-to)2329-2350
Number of pages22
JournalProceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
Volume463
Issue number2085
DOIs
StatePublished - 8 Sep 2007

Keywords

  • Asymmetric Stokes flow
  • Exact solution
  • Fredholm integral equation
  • Fused spheres
  • Mehler-Fock transform of general order
  • Three-contour equation

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