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Slow viscous motion of a solid particle in a spherical cavity

A. Sellier1
LadHyX, Ecole Polytechnique, FRANCE

Computer Modeling in Engineering & Sciences 2008, 25(3), 165-180. https://doi.org/10.3970/cmes.2008.025.165

Abstract

The slow viscous and either imposed or gravity-driven migration of a solid arbitrarily-shaped particle suspended in a Newtonian liquid bounded by a spherical cavity is calculated using two different boundary element approaches. Each advocated method appeals to a few boundary-integral equations and, by contrast with previous works, also holds for non-spherical particles. The first procedure puts usual free-space Stokeslets on both the cavity and particle surfaces whilst the second one solely spreads specific Stokeslets obtained elsewhere in Oseen (1927) on the particle's boundary. Each approach receives a numerical implementation which is found to be in excellent agreement with accurate results available for spherical particles. The computations for spheroidal or ellipsoidal particles, here accurately achieved at a very reasonable cpu time cost using the second technique, reveal that the particle settling migration deeply depends upon the gravity and upon both its shape and location inside the cavity.

Keywords

stokes flow, wall-particle interactions, spherical cavity, sedimentation, Green tensor, boundary-integral equations

Cite This Article

Sellier, A. (2008). Slow viscous motion of a solid particle in a spherical cavity. CMES-Computer Modeling in Engineering & Sciences, 25(3), 165–180.



This work is licensed under a Creative Commons Attribution 4.0 International License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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