Symmetry properties of nonlinear hydrodynamic interactions between responsive particles

TL;DR

This paper investigates how nonlinear hydrodynamic interactions between responsive particles can lead to relative motion and break time-reversal symmetry, with implications for particle dispersion and assembly.

Contribution

It provides a general analysis of symmetry properties of nonlinear hydrodynamic interactions, including specific examples demonstrating how these interactions can induce relative translation.

Findings

Nonlinear hydrodynamic interactions depend on system symmetries.

Time-reversal symmetry can be broken by nonlinear effects.

Examples show relative motion arises in various driven particle systems.

Abstract

Two identical particles driven by the same steady force through a viscous fluid may move relative to one another due to hydrodynamic interactions. The presence or absence of this relative translation has a profound effect on the dynamics of a driven suspension consisting of many particles. We consider a pair of particles which, to linear order in the force, do not interact hydrodynamically. If the system possesses an intrinsic property (such as the shape of the particles, their position with respect to a boundary, or the shape of the boundary) which is affected by the external forcing, hydrodynamic interactions that depend nonlinearly on the force may emerge. We study the general properties of such nonlinear response. Analysis of the symmetries under particle exchange and under force reversal leads to general conclusions concerning the appearance of relative translation and the motion's time-reversibility. We demonstrate the applicability of the conclusions in three specific examples: (a) two spheres driven parallel to a wall; (b) two deformable objects driven parallel to their connecting line; and (c) two spheres driven along a curved path. The breaking of time-reversibility suggests a possible use of nonlinear hydrodynamic interactions to disperse or assemble particles by an alternating force.