Percolating and nonpercolating liquid phase continuum model of drying in capillary porous media with application to solute transport in the very low Péclet number limit

Abstract

A three equation continuum model of drying is presented. The model explicitly considers the liquid phase as formed by a percolating liquid phase and a non-percolating liquid phase. The model is tested against pore network simulations. A quite good agreement is obtained between the predictions of the continuum model and data obtained by volume averaging the pore network simulation results. Then, the model is extended to the case where a solute is present in the liquid phase. This leads to the consideration of a five equation continuum model as opposed to the classically considered two equation model. The model is tested when diffusion is the solute dominant transport mechanism. In agreement with the pore network simulations, the five equation continuum model predicts that the solute concentration in the percolating liquid phase is greater than in the non-percolating liquid phase in the considered situation. The work illustrates the key role of the liquid fragmentation process occurring during drying on the solute dynamics. Counter-intuitively, although diffusion is dominant, it is shown that the solution concentration varies over the liquid phase as the result of the liquid phase fragmentation process.