Characteristic lengths affecting evaporative drying of porous media.

Evaporation from porous media involves mass and energy transport including phase change, vapor diffusion, and liquid flow, resulting in complex displacement patterns affecting drying rates. Force balance considering media properties yields characteristic lengths affecting the transition in the evaporation rate from a liquid-flow-based first stage limited only by vapor exchange with air to a second stage controlled by vapor diffusion through the medium. The characteristic lengths determine the extent of the hydraulically connected region between the receding drying front and evaporating surface (film region) and the onset of flow rate limitations through this film region. Water is displaced from large pores at the receding drying front to supply evaporation from hydraulically connected finer pores at the surface. Liquid flow is driven by a capillary pressure gradient spanned by the width of the pore size distribution and is sustained as long as the capillary gradient remains larger than gravitational forces and viscous dissipation. The maximum extent of the film region sustaining liquid flow is determined by a characteristic length L_{C} combining the gravity characteristic length L_{G} and viscous dissipation characteristic length L_{V} . We used two sands with particle sizes 0.1-0.5 mm ("fine") and 0.3-0.9 mm ("coarse") to measure the evaporation from columns of different lengths under various atmospheric evaporative demands. The value of L_{G} determined from capillary pressure-saturation relationships was 90 mm for the coarse sand and 140 mm for the fine sand. A significant decrease in drying rate occurred when the drying front reached the predicted L_{G} value (viscous dissipation was negligibly small in sand and L_{C} approximately L_{G} ). The approach enables a prediction of the duration of first-stage evaporation with the highest water losses from soil to the atmosphere.