SINGLE-PHASE FLOWS IN SWELLING, LIQUID-ABSORBING POROUS MEDIA: A DERIVATION OF FLOW GOVERNING EQUATIONS USING THE VOLUME AVERAGING METHOD WITH A NONDETERMINISTIC, HEURISTIC APPROACH TO ASSESSING THE EFFECT OF SOLID-PHASE CHANGES

A novel theoretical derivation of governing equations for single-phase flow of Newtonian fluids in swelling, liquid-absorbing porous media is performed. Some unique forms of mass balance (continuity) and momentum balance (Darcy's law) are developed using the volume averaging method. Solid-phase distribution is not predicted and is expected to be determined from in situ microscopic studies of the concerned porous media. The intake of flowing liquid into constituent particles or fibers leads to suspension of the no-slip boundary condition on their surfaces, resulting in new equation forms. The volume averaging of the continuity equation leads to the generation of sink and source terms; the equation is simplified further by defining an absorption coefficient b. The case of b being unity, which corresponds to the liquid absorption rate being equal to the particle expansion rate, results in the classic form of the continuity equation. In the proposed macroscopic equations as well as in the corresponding closure formulation, inertial terms are shown to be insignificant through order-of-magnitude analyses. The final formulation, which can be solved in a periodic unit cell in the absence of a significant porosity gradient, reveals a method to estimate macroscopic permeability using pore-scale topology, thus establishing an effective micro-macro coupling for the posed problem. The continuity equation, in conjunction with Darcy's law, explains quite well the experimental results observed during wicking of liquids into absorbent paper as well as observed during pressurized injection of liquids into swelling porous media made from natural fibers.