Slow viscous motion of a solid particle in a spherical cavity
A. Sellier

doi:10.3970/cmes.2008.025.165
Source CMES: Computer Modeling in Engineering & Sciences, Vol. 25, No. 3, pp. 165-180, 2008
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Keywords Stokes flow, wall-particle interactions, spherical cavity, sedimentation, Green tensor, boundary-integral equations.
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 \relax \begingroup \catcode `\ 12\relax \catcode `\\12\relax \catcode `\$12\relax \catcode `\&12\relax \catcode `\#12\relax \catcode `\^12\relax \catcode `\_12\relax \catcode `\%12\relax \catcode `\~12\relax \endgroup \relax \cite *{Oseen} 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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