Symmetry properties of nonlinear hydrodynamic interactions between responsive particles.

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.

Permeability of immobile rings of membrane inclusions to in-plane flow.

We study the flow of membranal fluid through a ring of immobile particles mimicking, for example, a fence around a membrane corral. We obtain a simple closed-form expression for the permeability coefficient of the ring as a function of the particles' line fraction. The analytical results agree with those of numerical calculations and are found to be robust against changes in particle number and corral shape. From the permeability results, we infer the collective diffusion coefficient of lipids through the ring and discuss possible implications for collective lipid transport in a crowded membrane.

Many-particle mobility and diffusion tensors for objects in viscous sheets.

We derive a mobility tensor for many cylindrical objects embedded in a viscous sheet. This tensor guarantees a positive dissipation rate for any configuration of particles and forces, analogous to the Rotne-Prager-Yamakawa tensor for spherical particles in a three-dimensional viscous fluid. We test our result for a ring of radially driven particles, demonstrating the positive-definite property at all particle densities. The derived tensor can be utilized in Brownian dynamics simulations with hydrodynamic interactions for such systems as proteins in biomembranes and inclusions in free-standing liquid films.

Hydrodynamic pair attractions between driven colloidal particles.

Colloidal spheres driven through water along a circular path by an optical ring trap display unexpected dynamical correlations. We use Stokesian dynamics simulations and a simple analytical model to demonstrate that the path's curvature breaks the symmetry of the two-body hydrodynamic interaction, resulting in particle pairing. The influence of this effective nonequilibrium attraction diminishes as either the temperature or the stiffness of the radial confinement increases. We find a well-defined set of dynamically paired states whose stability relies on hydrodynamic coupling in curving trajectories.