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 ( σ ¯ ) of the instabilities and their average wave number ( k ¯ ). Special attention is paid to the effects of two parameters, the solid fraction (0.10 ≤ ϕ 0 ≤ 0.40) of the granular suspension and the solid-to-fluid density ratio (1.5 ≤ R ≤ 2.7). Perturbations at the interface are observed to undergo a period of linear growth, the duration of which decreases with ϕ 0 and scales with the particle shear time d / w ∞ , where d is the particle diameter and w ∞ is the terminal velocity. For ϕ 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 ϕ 0 > 0.10 and appears independent of R. For a given ϕ 0 , the growth rate is found to be inversely proportional to the particle shear time, i.e., σ ¯ ∝ (d / w ∞) − 1 ; at a given R , σ ¯ increases monotonically with ϕ 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 ∞ to the evolution of interfacial granular RTI, highlight the various effects of ϕ 0 and R on these instabilities, and demonstrate modest applicability of the continuum-based LSA for the particle-laden problem. [ABSTRACT FROM AUTHOR]