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.
Highlights
The modeling of quasi-static processes of non-wetting liquid intrusion into porous material plays an important role in the interpretation of experimental data for mercury porosimetry obtained by mercury intrusion into a sample of porous material [22,23]
In mercury porosimetry, which is used by default to determine pore size distributions, the interpretation of experimental data is performed based on the capillary model of the pore space architecture
The model assumes that the quasi-static process of liquid intrusion takes place in the pore space-pressure continuum, that liquid filling an undeformable porous material forms a macroscopic continuum constituted by mobile liquid and capillary liquid and that the skeleton pore structure is isotropic
Summary
The modeling of quasi-static processes of non-wetting liquid intrusion into porous material plays an important role in the interpretation of experimental data (the so-called capillary potential curves) for mercury porosimetry obtained by mercury intrusion into a sample of porous material [22,23]. The pore space is formed by long capillaries of constant randomly distributed diameters that cross the whole sample This provides a very simple description of the processes of mercury intrusion and allows direct interpretation of the experimental data. The direct application of theories describes liquid transport in unsaturated porous materials to solve this problem, such as Richard’s equations [16], produces results identical to those for the medium with capillary pore space architecture This results from the assumption commonly taken in papers in this field that the capillary pressure is a constitutive quantity and is a unique function of saturation with liquid. The model assumes that the quasi-static process of liquid intrusion takes place in the pore space-pressure continuum, that liquid filling an undeformable porous material forms a macroscopic continuum constituted by mobile liquid and capillary liquid and that the skeleton pore structure is isotropic. Their dependence on parameters of the system is analyzed and the results are presented in the form of graphs
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