Hydrodynamic interactions of spherical particles in Poiseuille flow between two parallel walls

TL;DR

This study investigates the complex hydrodynamic interactions of spherical particles in Poiseuille flow between parallel walls, emphasizing the importance of far-field effects for accurate modeling of particle arrays.

Contribution

It introduces a highly accurate numerical algorithm to analyze hydrodynamic interactions of particles in wall-bounded flow, highlighting the significance of far-field contributions.

Findings

Pair interactions depend on interparticle distance and wall effects.

Crossover between different far-field asymptotic regimes identified.

Far-field flow influences force distribution in particle arrays.

Abstract

We study hydrodynamic interactions of spherical particles in incident Poiseuille flow in a channel with infinite planar walls. The particles are suspended in a Newtonian fluid, and creeping-flow conditions are assumed. Numerical results, obtained using our highly accurate Cartesian-representation algorithm [Physica A xxx, {\bf xx}, 2005], are presented for a single sphere, two spheres, and arrays of many spheres. We consider the motion of freely suspended particles as well as the forces and torques acting on particles adsorbed at a wall. We find that the pair hydrodynamic interactions in this wall-bounded system have a complex dependence on the lateral interparticle distance due to the combined effects of the dissipation in the gap between the particle surfaces and the backflow associated with the presence of the walls. For immobile particle pairs we have examined the crossover between several far-field asymptotic regimes corresponding to different relations between the particle separation and the distances of the particles from the walls. We have also shown that the cumulative effect of the far-field flow substantially influences the force distribution in arrays of immobile spheres. Therefore, the far-field contributions must be included in any reliable algorithm for evaluating many-particle hydrodynamic interactions in the parallel-wall geometry.