Numerical Solution of Wetting Fluid Spread into Porous Media

Purpose – The purpose of this paper is to develop a general numerical solution for the wetting fluid spread into porous media that can be used in solving of droplet spread into soils, printing applications, fuel cells, composite processing. Design/methodology/approach – A discrete capillary network model based on micro-force balance is numerically implemented and the flow for an arbitrary capillary number can be solved. At the fluid interface, the boundary condition that accounts for the capillary pressure jump is used. Findings – The wetting fluid spread into porous medium starts as a single-phase flow, and after some particular number of the porous medium characteristic length scales, the multi-phase flow pattern occurs. Hence, in the principal flow direction, the phase content (saturation) decreases, and in the lower limit for the capillary number sufficiently small, the saturation should become constant. This qualitative saturation behavior is observed irrespective of the flow dimensionality, whereas the quantitative results vary for different flow systems. Research limitations/implications – The numerical solution has to be expanded to solve the spread of the fluid in the porous medium after there is no free fluid left at the porous medium surface. Practical implications – It is shown that the multi-phase flow can develop even on a small domain due to the porous medium heterogeneity. Neglecting the medium heterogeneity and flow type can lead to a large error as shown for the droplet spread time in the porous medium. Originality/value – This is believe to be the only paper relating to solving the droplet spread into porous medium as a multi-phase flow problem.