Modeling Rayleigh-Taylor Instability of a Sedimenting Suspension Arising in Direct Numerical Simulation

In this paper we study the sedimentation of 6400 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 instability. The waves have a welldefined wavelength and growth rate which can be modeled as a conventional RayleighTaylor 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 effective viscosity of the solid-liquid dispersion. The results of the simulation are in satisfying agreement with results predicted by the model using viscous potential flow without fitting parameters.