Accurate treatment of lubrication forces between rigid spheres in viscous fluids using a traction-corrected boundary element method

Abstract

Traditional boundary element methods cannot accurately resolve lubrication forces in the interstitial regions between nearly touching particles in viscous flows. In many cases, the interstitial tractions are underestimated and the relative particle velocities are overestimated resulting in significant errors in predicting particle trajectories. In order to accurately treat the lubrication forces between nearly touching particles, a traction-corrected boundary element method (TC-BEM) for multiple particles is developed by combining the analytical asymptotic solution for the tractions in the interstitial regions with the boundary element method. An adaptive meshing algorithm is developed to provide appropriate meshes on surfaces of particles with close interactions. The numerical method also employs an efficient parallelization scheme to make possible prediction of long-time behavior of particles suspended in viscous flow fields. The results of the TC-BEM are benchmarked by comparisons to analytical results for two particles in a linear shear flow and by considering the reversibility of three particles in a circular Couette flow. It is shown that the TC-BEM is able to correctly resolve the lubrication forces between nearly touching particles, thus enabling the accurate analysis of particles suspended in nonlinear shear flows.