Instabilities in two-dimensional suspension flows

We study the emergence of miscible fingering in quasi-two-dimensional suspension flows, by combining experiments and theory. We experimentally inject silicone oil into the mixture of the same oil and non-colloidal particles inside a highly confined channel. The gap thickness is comparable to the particle diameter, so that suspended particles form a monolayer inside the cell. Our experiments reveal that miscible fingering is observed at all concentrations, distinct from the continuum limit. In addition, the emergent fingers exhibit concentration-dependent wavelengths as well as continuous particle fluctuations, reminiscent of 2D droplet ensembles. To rationalize our observations, we develop a kinetic theory that implements long-range hydrodynamic interactions between highly confined particles. The theory qualitatively predicts the experimental observations.