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.

Hydrodynamic interactions between two forced objects of arbitrary shape. I. Effect on alignment

“…In that section we also provided a possible explanation for this repulsion, related to the mutual rotation of the two objects which causes them to glide away from each other. In fact, the objects need not be irregular to exhibit this gliding effect; two forced ellipsoids which start parallel to one another will experience the same repulsion 20,29,46 . The resulting hydrodynamic "pseudo-potential"…”

Hydrodynamic properties of rigid fractal aggregates of arbitrary morphology

“…Recently, Chopard et al [32] estimated the hydrodynamic radius of 3D fractal aggregates with fractal dimension, d f , from 1.98 to 3.0 using Lattice Boltzmann method (LBM) by properly scaling Haimoto and Acrivos equation for friction factor and effective volume fraction of fractal aggregates in suspensions. Kutteh [33] has recently published an approach based on rigid body Stokesian dynamics (SD), offering an alternative to the conventional algorithms, such as HSHAKE, used to simulate constrain on a collection of particles to be part of a rigid body. The developed method was successfully used to follow the dynamic motion and trajectories of rigid aggregates of complex shapes, but was neither used to analyze the intrinsic hydrodynamic properties of commonly encountered fractal aggregates, nor did it give explicit expressions of the grand resistance matrix.…”

Stokesian dynamics simulation of sub-micron hydrodynamically interacting nonspherical particles

“…In seeking a solution to the problem of describing the SD of such a general system within a rigid body dynamics formalism, two alternative strategies can be employed [11]. One strategy consists of casting the problem in the framework of rigid body Newtonian dynamics, into which the necessary elements of the SD of spheres are then introduced in order to describe the SD of a general system containing rigid groups of spheres and free spheres.…”

“…To address (i) and (ii), we describe next an alternative algorithm for SD simulations of arbitrary shape rigid particles with HI, modeled again as rigid groups of spheres, with hydrodynamic mobility readily computable to high accuracy by any of the existing schemes for spheres. This algorithm is based on rigid body equations of motion we have derived [11] for a general SD system of rigid groups of spheres and free spheres. …”