Instabilities induced by concentration gradients in dusty gases

Abstract

This paper deals with the stability of suspensions modelled as dusty gases for non-uniform profiles of mass fraction of particles. It is known that a stationary uniform fluidized bed may be unstable to small disturbances which grow until a secondary instability develops forming bubbles that rise through the bed. Interactions between particles are difficult to model and this makes it necessary to close the model with some assumptions. However, in dilute fluidized beds which are characterized by a low volume fraction of particles, interactions between particles are negligible and this motivates the study of instabilities of suspensions by means of the dusty gas equations, avoiding the problem of particular closures.We show in this work that suspensions blown to regions of higher concentration are unstable to two-dimensional disturbances. An equation which governs this instability is obtained. A physical mechanism is proposed to explain this instability and it is related to the Rayleigh–Taylor one in the limit of long characteristic lengthscales associated with the concentration profile. Finally, the evolution of this instability is followed using a fully nonlinear numerical code showing the formation of streamers and clusters of particles.