Enhanced mixing via alternating injection in radial Hele-Shaw flows

Mixing at low Reynolds numbers, especially in the framework of confined flows occurring in Hele-Shaw cells, porous media, and microfluidic devices, has attracted considerable attention lately. Under such circumstances, enhanced mixing is limited due to the lack of turbulence, and absence of sizable inertial effects. Recent studies, performed in rectangular Hele-Shaw cells, have demonstrated that the combined action of viscous fluid fingering and alternating injection can dramatically improve mixing efficiency. In this work, we revisit this important fluid mechanical problem, and analyze it in the context of radial Hele-Shaw flows. The development of radial fingering instabilities under alternating injection conditions is investigated by intensive numerical simulations. We focus on the impact of the relevant physical parameters of the problem (Péclet number Pe, viscosity contrast A, and injection time interval Δt) on fluid mixing performance.