Reaction-driven oscillating viscous fingering

Localized oscillations can develop thanks to the interplay of reaction and diffusion processes when two reactants $A$ and $B$ of an oscillating reaction are placed in contact, meet by diffusion, and react. We study numerically the properties of such an $A+B→$ oscillator configuration using the Brusselator model. The influence of a hydrodynamic viscous fingering instability on localized concentration oscillations is next analyzed when the oscillating chemical reaction changes the viscosity of the solutions involved. Nonlinear simulations of the related reaction–diffusion–convection equations with the fluid viscosity varying with the concentration of an intermediate oscillatory species show an active coupling between the oscillatory kinetics and the viscously driven instability. The periodic oscillations in the concentration of the intermediate species induce localized changes in the viscosity, which in turn can affect the fingering instability. We show that the oscillating kinetics can also trigger viscous fingering in an initially viscously stable displacement, while localized changes in the viscosity profile can induce oscillations in an initially nonoscillating reactive system.