Stripes instability of an oscillating non Brownian iso-dense suspension of spheres
We analyze experimentally the behavior of a non-Brownian, iso-dense suspension of spheres submitted to periodic square wave oscillations of the flow in a Hele-Shaw cell of gap $H$. We do observe an instability of the initially homogeneous concentration in form of concentration variation stripes transverse to the flow. The wavelength of these regular spatial structures scales roughly as the gap of the cell and is independent of the particle concentration and of the period of oscillation. This instability requires large enough particle volume fractions $ϕ\geq 0.25$, a gap large enough compared to the spheres diameter ($H/d \geq 8$) and is observed in a rather broad range of periods of the square waves and amplitudes of the fluid displacement. We map the domain of existence of this instability in the space of the control parameters. The analysis of the concentration distribution across the gap shows that the instability is likely to be associated to the migration of the particles from the center towards the cell walls. In order to account for the main features of this stripes instability, we use the theory of longitudinal instability due to normal stresses difference and recent measurements of the first normal stresses difference dependence with particles concentration.