Stokesian simulation of two unequal spheres in a pressure-driven creeping flow through a cylinder

Abstract

In this paper, a novel numerical technique is generalized for analysis of mutual flow interactions between unequal particles in cylinder-bound pressure-driven flow of highly viscous fluid. The methodology is general enough to account for any polydisperse many-sphere system confined in a circular channel. The scheme is especially useful for the geometric configurations where both interparticle and particle-wall hydrodynamic interactions are significant. In such situation, particulate dynamics is governed by strong spatial variation of mobility tensors relating motion-inducing quantities (like force and torque on the bodies along with the pressure-drop in the vessel) to motion-defining ones (like translational and rotational velocities of each sphere as well as the flow-rate). Accordingly, the mobility tensors are evaluated as spatial functions to solve two different problems. First, we compute force and torque due to incoming fluid on two particles when these are fixed at a specific position inside the flow-domain. Then, we assume both to be freely suspended, and determine their motion driven by the transporting medium. In both problems, the additional pressure-loss in the channel due to the presence of the particles is also calculated representing the increase in channel-resistivity and effective viscosity, respectively.