Rayleigh-Taylor instability in size-bidisperse isodense granular flow down an incline.

Abstract

Size-bidisperse granular material flowing down a rough incline, or chute, may develop a Rayleigh-Taylor instability even when the two particle species have the same density. Unlike fluid instability, which occurs under quiescent conditions, the granular material must be flowing for the instability to occur. Initially, size segregation results in a monodisperse layer of large particles above a monodisperse layer of small particles with an interfacial layer of mixed particles that has a higher volume fraction and, hence, is denser than the monodisperse layers above and below it. The interfacial layer destabilizes via a Rayleigh-Taylor instability and forms dense descending plumes of mixed particles and ascending plumes of less dense pure small particles. As a result of these plumes, the upper layer of large particles breaks and accumulates above the descending plumes; the small-particle plumes reach the free surface. The instability evolves into persistent longitudinal rolls corresponding to streamwise bands, or stripes, of small and large particles at the free surface. The appearance of the instability depends on the particle and mixture properties as well as the flow conditions. In all cases, the propensity for the appearance of the instability and subsequent band formation can be traced back to the total particle volume fraction, or packing density, in the mixed-particle layer, which depends on the particle size ratio, fraction of each particle species, and thickness of the flow.