Hydrodynamic interactions suppress deformation of suspension drops in Poiseuille flow

Abstract

Evolution of a suspension drop entrained by Poiseuille flow is studied numerically at a low Reynolds number. A suspension drop is modelled by a cloud of many non-touching particles, initially randomly distributed inside a spherical volume of a viscous fluid which is identical to the host fluid outside the drop. Evolution of particle positions and velocities is evaluated by the accurate multipole method corrected for lubrication, implemented in the {\sc hydromultipole} numerical code. Deformation of the drop is shown to be smaller for a larger volume fraction. At high concentrations, hydrodynamic interactions between close particles significantly decrease elongation of the suspension drop along the flow in comparison to the corresponding elongation of the pure-fluid drop. Owing to hydrodynamic interactions, the particles inside a dense-suspension drop tend to stay for a long time together in the central part of the drop; later on, small clusters occasionally separate out from the drop, and are stabilized by quasi-periodic orbits of the constituent non-touching particles. Both effects significantly reduces the drop spreading along the flow. At large volume fractions, suspension drops destabilize by fragmentation, and at low volume fractions, by dispersing into single particles