J. Fluid Mech. (2001), vol. 434, pp. 23-37. Printed in the United Kingdom

2001 Cambridge University Press

 

Modelling Rayleigh-Taylor instability

of a sedimenting suspension of

several thousand circular particles

in a direct numerical simulation

 

By T. W. PAN1, D. D. JOSEPH2 AND R. GLOWINSKI1

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

2Aerospace Engineering and Mechanics, University of Minneapolis, 107 Ackerman Hall,

110 Union Street, Minneapolis, MN 55455, USA

(Received 7 September 1999 and in revised form 9 October 2000)

 

In this paper we study the sedimentation of several thousand circular particles in two dimensions 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 modelled as a composite solid-liquid fluid with an effective composite density and viscosity. Surface tension cannot enter this problem and the characteristic shortwave 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 & Beavers (1999) to a rectangular domain bounded by solid walls; an exact solution is obtained.