Unstable oscillatory flow of non-Brownian suspensions in Hele-Shaw cells

The behavior of neutrally buoyant, non-Brownian suspensions subject to square-wave flow oscillations in Hele-Shaw cells is investigated. The velocity field across the cell gap is determined by tracking particles in a plane parallel to the main flow. Initially, the velocity field of the particles is parallel to the main flow and its profile across the gap is blunted due to a higher volume fraction of particles in the gap center; this has been confirmed by direct estimations of the particle fraction and likely results from shear-induced migration. Velocity fluctuations, both along and transverse to the flow direction, agree reasonably well with previous studies. At longer times, the suspension develops an instability characterized by the growth of a transverse velocity component that is periodic along the main flow direction and in time. No influence of inertia on the characteristic onset time of this instability is observed for Reynolds numbers varying over four decades below Re = 0.4. The inverse of the onset time increases linearly with the amplitude of the oscillatory flow. The dependence of the onset time on the particle volume fraction and the gap thickness is consistent with the characteristic time for particle migration across the gap due to shear-induced diffusion.