Convection induced by centrifugal and Coriolis buoyancy in a rotating Hele-Shaw reactor

The study of heat and mass transfer in a Hele-Shaw cell rotating around a perpendicular axis has various advanced technological applications. These include the design of microfluidic devices and continuous-flow chemical microreactors, to name a couple. In this setup configuration, the quasi-two-dimensional design allows for recording the density field using optical methods, and the rotation enables control of this field through spatially distributed inertial forces. As is known, in the limit of an infinitely thin layer, the Coriolis force vanishes within a standard mathematical model. However, experimental observations of fluid flow in a rotating Hele-Shaw cell indicate the opposite. In this paper, we show that the correct derivation of the equation of motion under the Hele-Shaw approximation leads to the appearance of a Boussinesq-type term for the Coriolis force. To study the effect of the Coriolis buoyancy, we consider the problem of fluid stability during the internal generation of a transfer component, which can be either the concentration of the dissolved substance or the temperature of the medium. The careful study of system dynamics involves linear stability analysis, weakly nonlinear analysis, and direct numerical simulation. The general properties of the disturbance spectrum are analyzed. The branching of solutions near the first bifurcation is studied using the technique of multiple time scales. A stationary convection is replaced by an oscillatory one under the action of the Coriolis force, as demonstrated by weakly nonlinear analysis. Finally, we investigate the nonlinear dynamics using direct numerical simulation.