Stokes flow past three spheres

In this paper we present a numerical method to calculate the dynamics of three spheres in a quiescent viscous fluid. The method is based on Lamb’s solution to Stokes flow and the Method of Reflections, and is arbitrarily accurate given sufficient computer memory and time. It is more accurate than mu...

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Bibliographic Details
Published in:Journal of computational physics 2013-07, Vol.245, p.302-316
Main Author: Wilson, Helen J.
Format: Article
Language:English
Subjects:
Convergence
Dynamics
Handles
Mathematical analysis
Mathematical models
Method of Reflections
Multipoles
Reflection
Spherical particles
Stokes flow
Stokesian Dynamics
Viscous flow
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Summary:In this paper we present a numerical method to calculate the dynamics of three spheres in a quiescent viscous fluid. The method is based on Lamb’s solution to Stokes flow and the Method of Reflections, and is arbitrarily accurate given sufficient computer memory and time. It is more accurate than multipole methods, but much less efficient. Although it is too numerically intensive to be suitable for more than three spheres, it can easily handle spheres of different sizes. We find no convergence difficulties provided we study mobility problems, rather than resistance problems. After validating against the existing literature, we make a direct comparison with Stokesian Dynamics (SD), and find that the largest errors in SD occur at a sphere separation around 0.1 radius. Finally, we present results for an example system having different-sized spheres.
ISSN:0021-9991
1090-2716
DOI:10.1016/j.jcp.2013.03.020