Pattern Formation in Miscible Rotating Hele-Shaw Flows Induced by a Neutralization Reaction

Abstract

We study the centrifugal buoyancy-driven chemoconvection in a Hele-Shaw cell that uniformly rotates around e perpendicular axis. The slot is considered thin enough to neglect the influence of the Coriolis force. The initial configuration of the system consists of two aqueous reacting solutions separated by a concentric boundary. The acid solution fills the center of the cavity, while the base solution is in the periphery. Bringing liquids into contact initiates a neutralization reaction to form a salt. We show that reaction-diffusion processes produce a potential well near the reaction front, which determines the pattern formation of the system. For some ratios of initial concentrations, there appears a periodic sequence of chemoconvective vortices in the well, while for others, when the well collapses, a shock-like density wave occurs. When the density of the acid solution is higher, the Rayleigh-Taylor instability develops in the system. We found that an increase in the rotation speed leads to a gradual disruption of the structure periodicity. It can even result in the ejection of some vortices from the potential well. We show that the density wave is extremely sensitive to the magnitude of the centrifugal force, occurring only at some critical value. Finally, we obtained a stability map of the system by performing direct numerical simulations for increasing the centrifugal Rayleigh number and the dimensionless distance of the initial contact surface between the solutions from the axis of rotation.