Modelling Rayleigh-Taylor instability of a sedimenting suspension of several thousand circular particles in a direct numerical simulation. (English) Zbl 0985.76031

Summary: 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 modelled 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 short-wave instability is regularized by the viscosity of the solid-liquid dispersion. The dynamics of Rayleigh-Taylor instability is studied using viscous potential flow, and an exact solution is obtained.


76E17 Interfacial stability and instability in hydrodynamic stability
76T20 Suspensions
76M25 Other numerical methods (fluid mechanics) (MSC2010)
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