Theory of drying of polymer solutions in porous media

Plant roots and bacteria release in soils polymeric blends of substances which alter the physics of soil water flow and support life in soils. They adsorb water, decrease the surface tension of the soil solution and increase its viscosity, and, more generally, they change the soil solution into a non-Newtonian liquid with viscoelastic properties. A theory of drying of polymer solutions in porous media is missing and it is needed to understand the feedback between physics of porous media and life in soils. It was observed that during drying polymer solutions are deposited as thin surfaces spanning multiple pores and that these depositions are associated with a decrease in evaporation rate. Here, we provide a physical explanation of surface formation. The modeling framework includes Darcian flow across the polymeric network driven by a gradient in water potential. As the polymer dries and air invades the pore space the polymer network is stretched. The stretching causes a stress in the polymer network that alters the relation between water potential and polymer concentration: the more stretched is the polymer network the smaller is the spacing between the polymers at a given water potential, and the lower is the permeability of the network. The model predicts that at a critical point during evaporation there is an asymptotic increase in polymer concentration at the gas-gel interface corresponding to the deposition of solid-brittle interfaces. The onset of this glass transition depends on flow rate and pore size, with earlier deposition for fast high evaporative fluxes and small pores. The model explains why evaporation is suppressed much earlier and more significantly when the polymer solution dries into a porous medium, in comparison to the case when the polymer solution is free to dry outside a porous medium.