Particle interactions in oscillatory Stokes flow

It has been observed both experimentally and numerically for relatively dense suspension flows that small-amplitude oscillating Poiseuille flow results in particle migration towards the high shear rate region of the flow field (pipe walls), whereas, large-amplitude oscillating Poiseuille flow results in particle migration towards the low shear rate region of the flow field (pipe centerline). To date, there has been no satisfactory explanation as to why the period of oscillation has this effect on the direction of particle migration. In the current paper, we demonstrate through numerical simulation the same behavior in two-particle systems which provides a first principle explanation of at least one cause for this phenomenon in dense suspension flows. The numerical analysis is based on a semi-analytic solution for the motion of two spheres suspended in arbitrary, unbounded shear flow.