Influence of the Boundary Conditions on Capillary Flow Dynamics and Liquid Distribution in a Porous Medium

After depositing a wetting liquid onto a porous medium surface, and under the influence of the capillary pressure, the liquid is imbibed into the porous medium creating a wetted imprint. The flow within the porous medium does not cease once all the liquid is imbibed but continues as a secondary capillary flow, where the liquid flows from large pores into small pores along the liquid interface. The flow is solved using the capillary network model, and the influence of the boundary condition on the liquid distribution within the porous medium is investigated. The pores at the porous medium boundaries can be defined as open or closed pores, where an open pore is checked for the potential threshold condition for flow to take place. In contrast, the closed pore is defined as a static entity, in which the potential condition for flow to take place is never satisfied. By defining the pores at distinct porous medium boundaries as open or closed, one is able to obtain a very different liquid distribution within the porous medium. The liquid saturation profiles along the principal flow direction, ranging from constant to steadily decreasing, to the profile with a local maximum, are found numerically. It is shown that these saturation profiles are also related to the geometrical dimension that is perpendicular to the flow principal direction, and changing the boundary type from open to closed allows the liquid distribution within the porous medium to be controlled. In addition to the liquid distribution, the influence of the boundary conditions on capillary pressure and relative permeability is investigated, where both parameters are not influenced by variation of the boundary condition types