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 ≤ φ₀ ≤ 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 φ₀ and scales with the particle shear time d/w_∞, where d is the particle diameter and w_∞ is the terminal velocity. For φ₀ > 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 φ₀ > 0.10 and appears independent of R. For a given φ₀, 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 φ₀, 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 time scale d/w_∞ to the evolution of interfacial granular RTI, highlight the various effects of φ₀ and R on these instabilities, and demonstrate modest applicability of the continuum-based LSA for the particle-laden problem.