Continuum description of quasi-static intrusion of non-wetting liquid into a porous body

Abstract

This paper proposes a continuum description of the quasi-static processes of non-wetting liquid intrusion into a porous body. The description of such processes is important in the interpretation of mercury porosimetry data, which is commonly used to determine the pore space structure parameters of porous materials. A new macroscopic model of capillary transport of non-wetting liquid in porous material is proposed. It is assumed that a quasi-static process of liquid intrusion takes place in the pore space-pressure continuum and that liquid filling an undeformable porous material forms a macroscopic continuum constituted by a mobile and a capillary liquid which exchange mass and energy. The capillary liquid forms a thin layer on the surface of the liquid filling the porous material that is in contact with the internal surface of the pores. It is immoveable and contains the whole capillary energy. Mass balance equations for both constituents and constitutive relations describing capillary transport in the pore space-pressure continuum are formulated, and a boundary condition on the surface of the porous body is proposed. The equations obtained are solved for the special case of liquid intrusion into a ball of porous material. Analytical expressions are obtained for the saturation distribution of non-wetting liquid in the ball and for the capillary potential curve. Their dependence on parameters of the system is analyzed.