Rigid body dynamics approach to Stokesian dynamics simulations of nonspherical particles

Abstract

We describe an algorithm for performing Stokesian dynamics (SD) simulations of suspensions of arbitrary shape rigid particles with hydrodynamic interactions, modeled as rigid groups of spheres, the hydrodynamic mobility matrix of which is accurately computable by several established schemes for spheres. The algorithm is based on Stokesian rigid body equations of translational and rotational motion, which we have derived by an approach formally analogous to that of Newtonian rigid body dynamics. Particle orientation is represented in terms of Euler parameters (quaternion of rotation). This rigid body SD algorithm (RBSDA) complements recently described constraint SD algorithms [R. Kutteh, J. Chem. Phys. 119, 9280 (2003); R. Kutteh, Phys. Rev. E 69, 011406 (2004)], over which it offers the same computational advantages in imposing total rigidity that the basic rigid body molecular dynamics (MD) algorithm offers over constraint MD algorithms. We show that SD simulation results generated with the RBSDA, in bounded and unbounded geometries, agree very well with those from experiment and other SD and non-SD methods, and are numerically identical to those from a constraint SD algorithm, HSHAKE. Finally, for completeness we also describe a third (additional to the constraint SD and rigid body SD approaches) more traditional approach for SD simulations of arbitrary shape rigid particles modeled as rigid groups of spheres.