Rayleigh-Taylor instability in two-layer granular flows.

Abstract

Two layers of dry granular particles of different density are initially superimposed in an unstable configuration, the layer of dense particles above. This layering is set in motion, numerically by tilting the gravity in discrete element method simulations with periodic boundary conditions and experimentally by opening a confinement gate at the bottom of an inclined channel. In both cases, a Rayleigh-Taylor-like instability (RTI) is rapidly observed and plumes from the lower layer of light particles emerge at the free surface. Owing to the downslope mean flow and shear, these plumes organize themselves in a pattern of alternated bands of dense and light particles. Dense particles segregate toward the surface due to their larger size compared to lighter ones. This continuous transport at the free surface feeds the bands of dense particles and sustains longitudinal rolls underneath these bands. The granular RTI shares similarities with viscous fluid RTI, showing a wavelength proportional to flow thickness, a perturbation that grows exponentially and a growth rate increasing with density ratio. The two layers are miscible, yet, unlike fluids, two additional processes come into play, sedimentation that favors diffusion and size segregation that acts as an antidiffusion process. Both combine to control the extent of the diffusion zone at the interface between layers.