A Barrier Method for Contact Avoiding Particles in Stokes Flow

TL;DR

This paper introduces a barrier method to prevent particle overlaps in Stokes flow simulations by enforcing non-overlap constraints through a barrier energy, ensuring collision-free particle dynamics.

Contribution

The novel approach models non-overlap constraints with a barrier energy and computes contact forces to prevent overlaps in Stokes flow simulations.

Findings

Successfully prevents overlaps in simulations of spheres, rods, and boomerangs.

Maintains collision-free configurations at all simulation time steps.

Shows impact of contact forces on particle arrangements in flow.

Abstract

Rigid particles in a Stokesian fluid can physically not overlap, as a thin layer of fluid always separates a particle pair, exerting increasingly strong repulsive forces on the bodies for decreasing separations. Numerically, resolving these lubrication forces comes at an intractably large cost even for moderate system sizes. Hence, it can typically not be guaranteed that particle collisions and overlaps do not occur in a dynamic simulation, independently of the choice of method to solve the Stokes equations. In this work, non-overlap constraints, in terms of the Euclidean distance between boundary points on the particles, are represented via a barrier energy. We solve for the minimum magnitudes of repelling contact forces between any particle pair in contact to correct for overlaps by enforcing a zero barrier energy at the next time level, given a contact-free configuration at a previous instance in time. The method is tested using a multiblob method to solve the mobility problem in Stokes flow applied to suspensions of spheres, rods and boomerang shaped particles. Collision free configurations are obtained at all instances in time. The effect of the contact forces on the collective order of a set of rods in a background flow that naturally promote particle interactions is also illustrated.