Modeling Rayleigh-Taylor Instability of a Sedimenting Suspension of Several Thousand Circular Particles in Direct Numerical Simulation

T.W. Pan1, D.D. Joseph2, R. Glowinski1

1Department of Mathematics, University of Houston, Houston, TX 77204

2Aerospace Engineering and Mechanics, University of Minneapolis, 107 Akerman Hall, 110 Union Street, Minneapolis, MN 55455

Abstract

In this paper we study the sedimentation of several thousand circular particles in 2D using the method of distributed Lagrange multipliers for solid-liquid flow. The simulation gives rise to fingering which resembles Rayleigh-Taylor instabilities. The waves have a well defined wavelength and growth rate which can be modeled as a conventional Rayleigh-Taylor instability of heavy fluid above light. The heavy fluid is modeled as a composite solid{liquid fluid with an effective composite density and viscosity. Surface tension cannot enter this problem and the characteristic short wave instability is regularized by the viscosity of the solid liquid dispersion. The dynamics of the Rayleigh-Taylor instability are studied using viscous potential flow generalizing work of Joseph, Belanger, and Beavers (1999) to a rectangular domain bounded by solid walls; an exact solution is obtained.

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