Open Access

ARTICLE

Slow viscous motion of a solid particle in a spherical cavity

A. Sellier¹

1 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.

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