The role of temperature and drying cycles on impurity deposition in drying porous media

We consider a liquid containing impurities saturating a porous material; when the liquid evaporates, the impurities are deposited within the material. Applications include filtration and waterproof textiles. We present a mathematical model incorporating coupling between evaporation, accumulation and transport of the impurities, and the impact of the deposited impurities on the transport of both the suspended impurities and the liquid vapour. By simulating our model numerically, we investigate the role of temperature and repeated drying cycles on the location of the deposited impurities. Higher temperatures increase the evaporation rate so that impurities are transported further into porous material before depositing than for lower temperatures. We quantify two distinct parameter regimes in which the material clogs: (i) the dry-clogging (high-temperature) regime, in which impurities are pushed far into the material before clogging, and (ii) the wet-clogging (high-impurity) regime, in which liquid becomes trapped by the clogging. Clogging restricts the extent to which drying time can be reduced by increasing the temperature.