Interception of two spheroidal particles in shear flow

A numerical method is developed for simulating the motion of particles with arbitrary shape in an effectively infinite or bounded viscous flow. The particle translational and angular velocities are computed directly by solving an integral equation of the second kind arising from the double-layer representation for Stokes flow, subject to a specified force and torque. The deflated integral equation is solved by the method successive substitutions using a spectral boundary-element method. In the case of force- and torque-free particles, the contribution of the particles to the effective viscosity of the suspension is expressed in terms of the distribution density of the double-layer potential over the particle surfaces. The method is applied to investigate the interception of two spheroidal particles in simple shear flow, with emphasis on the net particle displacement and shift in the phase of rotation after separation, and on the transient signature of the interception on the effective viscosity of the suspension. The net particle displacement normal to the streamlines of the shear flow is found to have both positive and negative values depending on the relative particle configuration before interception. For moderate particle separations, the phase of rotation is shifted only slightly with respect to the Jeffery orbit executed by a particle in isolation.