Collision efficiency of non-Brownian spheres in a simple shear flow – the role of non-continuum hydrodynamic interactions

Abstract

We study the collisions in a gaseous medium of a dilute bidisperse suspension of non-Brownian spherical particles sedimenting along the flow axis of a simple shear flow. Continuum lubrication forces prevent particles from coming into contact in a finite time, thus collisions can occur only due to attractive interactions such as the van der Waals force. However, in a low-pressure medium, the lubrication forces are weaker than their continuum counterparts and allow particle pairs to collide, even without any attractive forces. The Knudsen number, defined as the ratio of the mean free path of the medium to the mean radius of the interacting spheres, captures the significance of non-continuum interactions. We use uniformly valid hydrodynamic mobility functions, reflecting non-continuum lubrication at small separations and full continuum hydrodynamic interactions at moderate to larger separations. Due to the nature of the pair trajectory topology, the collision efficiency vanishes at a critical Knudsen number when simple shear flow alone drives the dynamics. Thus we perform collision calculations where particles experience the combined effects of van der Waals attraction and non-continuum hydrodynamics; van der Waals interactions enable collisions below the critical Knudsen number. Next, we calculate the collision efficiency for coupled differential sedimentation and simple shear driven motion in the presence of van der Waals interaction and non-continuum hydrodynamics. Finally, we explore the role of small particle inertia on relative trajectories and collision efficiencies in a non-continuum gas subject to a simple shear flow, ignoring the van der Waals force and gravity.