Memory properties of fluid invasion in disordered media

Abstract

Fluid invasion through a porous medium exhibits interesting physical properties such as hysteresis and memory. In the ideal case where the invasion is driven quasistatically, and the passage from one equilibrium state to another is considered instantaneous, hysteresis cycles exhibit a property called Return Point Memory (RPM). This paper shows how to take into account the viscous pressure of the fluid and proves that the corresponding hysteresis cycles still exhibit RPM. In addition, a qualitative study of this viscous pressure based on a numerical solution of the balance equation is presented