Vibration effect on Rayleigh–Taylor instability of sedimenting suspension

In this paper, the effect of vertical vibration on the Rayleigh–Taylor instability at the lower interface of a sedimenting suspension layer sandwiched between viscous fluids is studied numerically and theoretically. It is shown numerically that the vibration suppresses the amplitudes of interface perturbations and enlarges the widths of granular fingers, postponing the nonlinear growth stage. By modeling the suspension as a fluid with its effective density and viscosity, stability analyses are carried out, and the dominant growth rate and the dominant wave number predicted by the dispersion relation agree with the numerical results, especially for cases with strong vibrations. Because of the small-scale flow induced by the particles, high vibration acceleration amplitude and low vibration frequency, which correspond to a large vibration power input, increase the kinetic energy spectra at the high wave number regime, a phenomenon contrary to the vibration effect for pure fluid cases.