Clustering and diffusion of suspended particles in an oscillatory straining flow

Particles experience oscillatory straining flows in a variety of situations, including flow in a wavy-walled conduit (such as a clothes dryer vent), colloidal particle transport through porous media, peristaltic transport, and particulate flows subject to acoustic excitation. Under the action of an oscillating straining flow, particulates exhibit a tendency to cluster at the center of straining due to the effects of particle inertia—a phenomenon referred to as oscillatory clustering. However, in the presence of a porous medium or other external bodies, particle oscillatory motion may be temporarily hindered. The capture-and-release events of random hindering act as a stochastic random walk, leading to diffusion of the particles in a process referred to as oscillatory diffusion. The current paper explores the dynamics of particulate flows subject to both oscillatory clustering and diffusion in both one and three dimensions using a stochastically perturbed discrete element method for particle simulation. The rates of clustering and diffusion are determined analytically, and situations exhibiting a combination of oscillatory clustering and diffusion are examined.