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Stokes flow for a shrinking pore

Published online by Cambridge University Press:  23 December 2015

Christopher A. Aubin  and
Rolf J. Ryham
Christopher A. Aubin
Affiliation:
Department of Physics and Engineering Physics, Fordham University, Bronx, NY 10458, USA
Rolf J. Ryham*
Affiliation:
Department of Mathematics, Fordham University, Bronx, NY 10458, USA
*
†Email address for correspondence: [email protected]
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Abstract

We consider a sphere with a circular pore embedded in an unbounded viscous fluid, where the rim of the pore moves in such a way that the radius of the sphere is constant. Away from the pore, the surface area stretches or compresses uniformly. An exact form for the axisymmetric velocity field which describes the quasi-static motion of the bulk fluid is calculated. The resulting dissipation function yields an analytical value for the aqueous drag coefficient for the sphere with a shrinking pore. Additionally, we examine the small hole and small angle limits, which converge to the unsteady flow for the expansion of a hole in a plane wall, and for the contraction of a circular disk.

JFM classification

Biological Fluid Dynamics: Biological Fluid Dynamics Low-Reynolds-number flows: Low-Reynolds-number flows Biological Fluid Dynamics: Membranes
Type
Papers
Information
Journal of Fluid Mechanics , Volume 788 , 10 February 2016 , pp. 228 - 245
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Copyright
© 2016 Cambridge University Press 

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