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

Abstract

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{less than or equal to}φ{less than or equal to}0.40) of the granular suspension and the solid-to-fluid density ratio (1.5{less than or equal to}R{less than or equal to}2.7). Perturbations at the interface are observed to undergo a period of linear growth, the duration of which decreases with φ and scales with the particle shear time d/w∞, where d is the particle diameter and w∞ is the terminal velocity. For φ>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 0.67d-1 for φ>0.10 and appears independent of R. For a given φ, 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, 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 φ and R on these instabilities, and demonstrate modest applicability of the continuum-based LSA for the particle-laden problem.

Harnessing Gravity‐Induced Instability of Soft Materials: Mechanics and Application

“…The instability of the interface evolves dynamically driven by the density difference and the acceleration of the fluids. The study of RT instability in solids is relevant to a lot of engineering applications, including transmission of sediments, [108,109] confinement fusion, [106,110] high-energy physics. [111] Additionally, RT instability provides insights into natural phenomena.…”