Double diffusive effects on radial fingering in a porous medium or a Hele-Shaw cell

Abstract

Double diffusive effects on the growth of radial viscous fingering in a porous medium or a Hele-Shaw cell were analyzed theoretically. Under linear stability theory, the stability equations were derived in a self-similar domain. The stability equations were transformed using the normal mode analysis and solved analytically and numerically. Regardless of the diffusivity ratio, Le, the Peclet number, Pe, makes the system unstable, i.e., accelerates the growth of instabilities. The double diffusive effects on the growth of the instabilities were strongly dependent on the viscosity distribution. If the displaced phase has stable viscosity distribution, as Le increases, the system becomes unstable regardless of the magnitude of Pe. However, as Le increases, the growth of the instabilities is suppressed if the displaced phase has unstable viscosity distribution.