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

Pan, T. W.; Joseph, D. D.; Glowinski, R.

J. Fluid Mech. 434, 23-37 (2001).

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.

MSC:

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

Keywords:

sedimenting suspension; direct numerical simulation; circular particles; method of distributed Lagrange multipliers; Rayleigh-Taylor instability; short-wave instability; solid-liquid dispersion; viscous potential flow; exact solution