Institute of Fundamental Technological Research

The evolution of linear arrays of rigid spheres and deformable drops in a Poiseuille flow between parallel walls is investigated to determine the effect of particle deformation on the collective dynamics in confined particulate flows. We find that linear arrays of rigid spheres aligned in the flow direction exhibit a particle-pairing instability and are unstable to lateral perturbations. Linear arrays of deformable drops also undergo the pairing instability but also exhibit additional dynamical features, including formation of transient triplets, cascades of pair-switching events, and the eventual formation of pairs with equal interparticle spacing. Moreover, particle deformation stabilizes drop arrays to lateral perturbations. These pairing and alignment phenomena are qualitatively explained in terms of hydrodynamic far-field dipole interactions that are insensitive to particle deformation and quadrupole interactions that are deformation induced. We suggest that quadrupole interactions may underlie the spontaneous formation of droplet strings in confined emulsions under shear

Simulations of over 10^3 hydrodynamically coupled solid spheres are performed to investigate collective motion of linear trains and regular square arrays of particles suspended in a fluid bounded by two parallel walls. Our novel accelerated Stokesian-dynamics algorithm relies on simplifications associated with the Hele-Shaw asymptotic far-field form of the flow scattered by the particles. The simulations reveal propagation of particle-displacement waves, deformation, and rearrangements of a particle lattice, propagation of dislocation defects in ordered arrays, and long-lasting coexistence of ordered and disordered regions.