Dynamic simulation of hydrodynamically interacting spheres in a quiescent second-order fluid

Abstract

A method is described for calculating the motion of N spherical particles suspended in a quiescent second-order fluid. The method requires calculation of only the low-Reynolds-number Newtonian velocity profile. This profile is used in conjunction with what has been called the ‘Reciprocal theorem method’ to evaluate particle velocities accurate to leading order in the Deborah number. If the Newtonian velocity field is found by a multipole moment expansion, then it is shown that the method can be integrated neatly into the Stokesian dynamics method of simulating Newtonian suspensions. Simulation results involving two, three, four and six particles are reported as illustrative examples, and are compared with corresponding results for particles in Newtonian fluids and with experimental results found in the literature. In addition, simulations of sedimenting suspensions are performed by using periodic boundary conditions to model an unbounded system, and the observed formation of clusters in the sedimenting system is shown to be in qualitative agreement with experimental observations.