Chemoconvective structures in a rotating system of reactive fluids

Abstract

Chemoconvective structures in a system of two reacting miscible liquids placed in a cylindrical Hele-Shaw cell that uniformly rotates around the axis of symmetry are studied. Previously, the behavior of similar system has been studied by the authors experimentally and theoretically under the static gravity field. A radially directed inertial field created by the centrifugal force varies in space (along the radius) and can be tuned by the rotation frequency, which gives the system new degrees of freedom. The initial configuration of the system consists of two concentric layers of aqueous solutions, initially separated in space by an infinitely thin diffusion zone. Solutions of acid and base are located respectively closer to the axis of rotation and at the periphery of the cell. The concentrations of reactants are selected in such a way as to guarantee the initial stability of the system with respect to Rayleigh-Taylor disturbances. After bringing fluids into contact, a neutralization reaction begins, which is accompanied by the production of salt. An important role is played by a concentration-dependent diffusion effect, which results in a nonlinear form of the corresponding transfer equations already for the base state characterized by the reaction-diffusion processes. As in the case of static gravity, there exists a density potential well near the reaction front, which determines the nonlinear dynamics of the system. A system of nonlinear equations describing the fluid motion is obtained. The results of numerical simulation of a complete nonlinear problem are presented. We show that cellular convection develops in the potential well at a certain ratio of the initial concentrations and the values of the centrifugal Rayleigh numbers. With an increase in the rotation speed, the periodicity of the structure is violated more and more due to the influence of the DLC instability, which arises near the axis of rotation, and the action of the inertial field, which ejects some cells from the potential well.