Transition to reaction-induced viscous fingering*

Viscous fingering (VF) occurs when a less viscous fluid displaces a more viscous one in porous media. Such instabilities appear both in the reactive and non-reactive fluids. Through the modification of the viscosity or density of the fluids or both and/or the permeability of the underlying porous medium, chemical reactions lead to a complex fingering dynamics in comparison to the non-reactive fluids. we show numerically that a second order chemical reaction of A + B → C causes a transition in the VF instability in miscible fluids. The reactants have equal viscosity and generate a product that has a dynamic viscosity different than the reactants. Using a hybridization of compact finite difference and pseudo-spectral methods numerical simulations of a radial source flow is performed. The VF patterns are in good agreement with the existing experiments. Radial displacement plays a significant role on the dynamics leading to various contrasting results from those existing for rectilinear displacements. We further show that the viscosity contrast due to chemical reactions is not always sufficient to trigger the instability and the instability region is summarized in a Da-Rc phase plane containing a stable zone sandwiched between two unstable zones.