Modelling evaporation-driven flows in capillary porous media

The evaporation of a liquid from within a capillary porous material (one in which capillary forces play a dominant role) is a complicated process involving coupled capillary flow, vapour diffusion, and phase-change. Different drying behaviours are observed at different stages during the process. Initially, liquid is drawn to the surface by capillary forces, where it evaporates at a near constant rate; thereafter a drying front recedes into the material, with a slower net evaporation rate. In this talk we derive mathematical models for this drying process by making systematically reducing an averaged continuum fluid-flow model, using the method of matched asymptotic expansions. Our analysis gives insight into the mechanisms that determine the overall drying timescale and the time of the transition from the constant-evaporation-rate period to the receding-front period of the drying process.