Equilibrium-State for Constant Concentration at Inlet Boundary in Porous Media Having Viscosity-Contrast

Understanding the Equilibrium State of Viscous Fingering Instability in Porous Media

Abstract

In porous media, displacement flows where two fluids are different in viscosity is much important for industry and biological applications. Due to viscosity-contrast between the fluids, instability is developed at the interface which is known as viscous fingering instability. In this work, we discussed about the equilibrium solution of the viscous-fingering instability problem. Advection-diffusion equation is obtained in equilibrium state. Hence, advection-diffusion is discussed in this paper which is fundamental in understanding of in- stability problem. Our result shows that in the early time, solution is not symmetric about the fluid-fluid interface. Our finding suggest that equilibrium state is time-dependent.