Fingering instabilities in binary granular systems

Abstract

Fingering instabilities akin to the Rayleigh-Taylor (RT) instability in fluids have been observed in a binary granular system consisting of dense and small particles layered on top of lighter and larger particles, when the system is subjected to vertical vibration and fluidizing gas flow. Using observations from experiments and numerical modelling we explore whether the theory developed to describe the Rayleigh-Taylor (RT) instability in fluids is also applicable to binary granular systems. Our results confirm the applicability of the classic RT instability theory for binary granular systems demonstrating that several key features are observed in both types of systems, viz: (i) The characteristic wavenumber of the instability is constant with time, (ii) the amplitude of the characteristic wavenumber initially grows exponentially and (iii) the dispersion relation between the wavenumbers k of the interface instability and the growth rates n(k) of their amplitudes holds in both fluid-fluid and binary granular systems. Our results also demonstrate that inter-particle friction is essential for the RT instability to occur in granular media. For zero particle friction the interface instability bears a greater resembles to the Richtmyer-Meshkov instability. We further define a yield criterion Y for the interface by treating the granular medium as a viscoplastic material; only for Y > 15 fingering occurs. Interestingly, previous work has shown that instabilities in the Earth's lower mantle, another viscoplastic material, also occur for similar values of Y.