Evolution of Rayleigh-Taylor instability at the interface between a granular suspension and a clear fluid

We report the characteristics of Rayleigh-Taylor instabilities (RTI) occurring at the interface between a suspension of granular particles and a clear fluid. The time evolution of these instabilities is studied numerically using coupled lattice Boltzmann and discrete element methods with a focus on the overall growth rate ((sigma) over bar) of the instabilities and their average wave number ((k) over bar). Special attention is paid to the effects of two parameters, the solid fraction (0.10 & LE; phi(0) & LE; 0.40) of the granular suspension and the solid-to-fluid density ratio (1.5 & LE; R & LE; 2.7). Perturbations at the interface are observed to undergo a period of linear growth, the duration of which decreases with phi(0) and scales with the particle shear time d/w(& INFIN;), where d is the particle diameter and w(& INFIN;) is the terminal velocity. For phi(0) > 0.10, the transition from linear to nonlinear growth occurs when the characteristic steepness of the perturbations is around 29%. At this transition, the average wave number is approximately 0.67 d(-1) for phi(0) > 0.10 and appears independent of R. For a given phi(0), the growth rate is found to be inversely proportional to the particle shear time, i.e., (sigma) over bar & PROP; (d/w(& INFIN;))(-1); at a given R , (sigma) over bar increases monotonically with phi(0), largely consistent with a linear stability analysis (LSA) in which the granular suspension is approximated as a continuum. These results reveal the relevance of the timescale d/w(& INFIN;) to the evolution of interfacial granular RTI, highlight the various effects of phi(0) and R on these instabilities, and demonstrate modest applicability of the continuum-based LSA for the particle-laden problem.