Granular instability in fluidized beds: A small-over-large instability

Abstract

For different particle diameters arranged in a gas fluidized bed, a new gravitational instability is predicted. The first order stability analysis yields conditions for growth of the most unstable wavenumber both as a function of particle diameter and dimensionless Bond number. Gravity acts to distribute the greater fluid mass associated with smaller particles, while surface tension stabilizes the entire bed against accelerations. The phenomenon, called the 'Small-over-Large' (SL) instability, evolves somewhat akin to a Rayleigh-Taylor mechanism and in addition to fundamental interest, carries implications for predicting solute redistribution and gravitational alignments in particle beds and chemical separation columns.