Interaction of foam with a porous medium: theory and calculations

A new theory of foam drainage in the presence of a porous support was introduced and accordingly, a mathematical model which combines the foam drainage equation with the equation describing imbibition into the porous substrate was developed. Proposed dimensionless equations were solved using finite element method. Boundary conditions were zero liquid flux on the top of the foam and continuity of flux on foam/substrate interface. It was found that the kinetics of foam drainage depends on three dimensionless numbers. The result indicated that there are two possible scenarios for the interaction of foam with a porous substrate: (i) a rapid imbibition, the liquid volume fraction at the bottom of the foam is a decreasing function of time. In this regime the imbibition into the porous substrate dominates and it is faster as compared with the foam drainage; (ii) a slow imbibition, the liquid volume fraction at the interface experiences a peak point and imbibition into the porous substrate is slower for some time as compared with the foam drainage.