Sessile droplet spread into porous substrates--determination of capillary pressure using a continuum approach

The problem of primary and secondary spread of sessile droplets into a porous substrate was formulated and solved numerically. A continuum approach for liquid- and gas-phases was utilized. The governing equations were discretized by finite difference method and solutions for both phases are obtained by marching in time using the fourth-order Runge-Kutta integration algorithm. This type of spread is a purely momentum-driven process that is caused by gradients both in capillary pressure and in saturation. A methodology was developed for finding the capillary pressure function for sessile droplets, which has not been described before. This approach was based on experimental data for a liquid/porous medium pair, and using universal, non-dimensional curves. Similar solutions were generated by the continuum approach and validated using experimental results. The model shows qualitative and quantitative agreement with experimental data. Although the focus of this work was to understand the interaction of chemical warfare agents with porous media, the approaches are universal and can be applied to determining the spread of any liquid into a porous material.