Fingering instability in particle systems

Abstract

In many multiphase systems, material interfaces can be destabilized by shocks. Small disturbances at these interfaces can grow in size to form large-scale fingers. We consider a shock propagating through a system that consists of two types of particles, of different mass, that are initially separated by an interface, but are free to mix. In the classical case of immiscible fluids, the finger of heavy fluid propagating into the light fluid grows faster and becomes much thinner than the finger of light fluid propagating into the heavy fluid. We show that collisions between particles of different types lead to shock focusing that causes a secondary flow that is initially similar to the fluid case. However, the particle system can exhibit completely different qualitative behavior in the nonlinear-growth phase and can give rise to the situation where the finger of heavy material is actually wider than the finger of the light material. We show that this qualitative change is due to a strong decompression that occurs in the heavy material. We also show that microscopic mixing can have an important impact on finger growth.