In porous media studies, imbibition is the spontaneous movement of a liquid into a porous medium under the influence of capillary forces. It is also known by the name wicking, and can sometimes be aided by an external pressure, as in the case of forced infiltration of liquid polymers into a bed of fibermats. In this study, the imbibition of liquids into porous media in important engineering applications is studied. A relatively new approach of using the single-phase flow behind a clearly-defined liquid front in a porous medium has been adopted in this work to model imbibition or wicking. Such an approach employs Darcy's law in conjunction with the continuity equation to model the liquid flow behind the front.

First the modeling of liquid flow in polymer wicks is undertaken. A new formula to predict the capillary suction-pressure at the liquid fronts in commercial wicks made of sintering the polymer beads was proposed. Later, a more general formula was derived and verified for estimating the capillary suction pressure in any kind of porous substance. We compared the performance of the proposed Darcy's-law based approach with that of the Lucas-Washburn equation; some new methods were suggested to improve the accuracy of these two dominant methods for modeling the liquid transport in aforementioned wicks.

Our Darcy's law based modeling approach is superior to the previous Washburn Equation based approaches as the former can be easily extended to 2-D and 3-D unlike the latter. The 3-D liquid flow in the wicks was studied numerically using PORE-FLOW^©, an in-house computer program to model porous-media flows. For the first time, the finite element/control volume (FE/CV) algorithm is employed to solve the moving- boundary problem encountered in wicking. A good validation is achieved against the 1-D wicking-flow analytical solution as well as a 3-D wicking experiment involving a wick with two different cross-sections.

A special case of wicking, in which both the external hydrodynamic pressure as well as the capillary suction-pressure are the drivers, was studied experimentally and modeled analytically. Both the Darcy's-law based approach as well as the Washburn-equation based approach were used as models. The former was shown to work better at zero or low external pressures, while the latter displayed good predictive capabilities at higher imposed pressures.

We also studied flow in non-rigid swelling porous media. The continuity equation was modified to include the liquid-absorption and swelling effects, and then Darcy's law was employed to model wicking in paper stripes made from cellulose and superabsorbent polymers. The proposed model showed very good agreement with previous experimental results. It was shown that the wicking predictions by the newly proposed model are identical to the predictions of another theoretical model in which Washburn equation was modified to include the swelling effects.

The wicking in swelling paper stripes was also modeled numerically using PORE-FLOW^©. Once again the continuity equation, modified to include the liquid-absorption and swelling effects, coupled with the Darcy's law formed the governing equations. The porosity and hence permeability in a swelling medium are a function of time in such a situation. A new method was proposed to estimate the local permeability in such swelling media from the absorbed-mass-vs-time plot to enable the numerical simulation of such a wicking process. The numerical results compared well with the experimental data and it proved the effectiveness of our suggested local-permeability estimation method as well as our wicking model for the swelling media.