Asymmetric creeping motion of a rigid spindle-shaped body in a viscous fluid

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Abstract

Exact solutions to the three-dimensional problems of asymmetric creeping translation and rotation of a rigid spindle-shaped body in a viscous incompressible fluid have been obtained. In both problems, the velocity field has been represented in the form of Dean and O'Neill, and under certain conditions, the equation of continuity has been reduced to a three-contour equation for an analytic function related to the density in a Fourier integral, representing the pressure in bispherical coordinates. Then, the three-contour equation has been reduced to a Fredholm integral equation of the second kind with a quasi-difference kernel by the complex Fourier transform. As an illustration for the obtained solutions, the pressure at the surface of the body has been calculated and analyzed. The resisting force and torque have been obtained for an arbitrary body of revolution via limits of certain harmonic functions at infinity and, as an example, have been computed for various values of a geometrical parameter of the spindle-shaped body for asymmetric translation and rotation, respectively.

Original languageEnglish
Pages (from-to)461-485
Number of pages25
JournalSIAM Journal on Applied Mathematics
Volume68
Issue number2
DOIs
StatePublished - 2007

Keywords

  • Asymmetric Stokes flow
  • Complex Fourier transform
  • Drag force
  • Exact solution
  • Fredholm integral equation
  • Resisting torque
  • Riemann boundary-value problem
  • Spindle-shaped body
  • Three-contour equation

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