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Modeling Rayleigh-Taylor Instability of a Sedimenting
Suspension of Several Thousand Circular Particles in Direct Numerical
Simulation
by T.W. Pan, D.D. Joseph, R. Glowinski
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.
The files are split due to the size of the simulation snapshots.
- RTI-thou-pp1-3.pdf (first
3 pages, 1.5 MB, PDF format)
- RTI-thou-p4.pdf (1 MB)
- RTI-thou-p5.pdf (1.8 MB)
- RTI-thou-pp6-9.pdf (1.8
MB)
- RTI-thou-pp10-23.pdf (1
MB)
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