Evaporation and condensation in soils: Experimental and modeling investigation to compare non-equilibrium-based approaches under different atmospheric boundary conditions

Evaporation and condensation in bare soils govern water and energy fluxes between the land and atmosphere. Despite their importance to the hydrologic cycle, there is great uncertainty associated with our understanding of these complex multiphase phenomena. At the representative elementary volume scale, phase change (i.e. evaporation/condensation) between water vapor and liquid water is commonly evaluated in soil hydrology using the equilibrium assumption. The equilibrium-based approach assumes that within the soil pores, phase change occurs instantaneously. However, finite volatilization/condensation times have been observed experimentally under certain conditions calling into question the validity of using the equilibrium assumption for all possible land-atmospheric interaction scenarios. The use of non-equilibrium mass transfer relationships is based on the Hertz-Knudsen (HK) equation derived from the kinetic theory of gases. Multiple formulations have been posited to numerically represent phase change between water vapor and liquid water, many relying on empirical fitting parameters. The purpose of this investigation was to perform an unbiased comparison between the various non-equilibrium phase change formulations using a fully coupled heat and mass transfer model that simulates the processes of evaporation/condensation from soils using precision generated laboratory data. A non-isothermal solution was implemented in a numerical model to account for five different non-equilibrium phase change formulations reported in literature. A series of five experiments were performed using a unique laboratory system consisting of a soil tank with controlled airflow boundary conditions at the soil surface. The apparatus was equipped with a sensor network for continuous and autonomous collection of soil moisture, soil and air temperature, relative humidity, and wind velocity data. Soil surface conditions (e.g. temperature, diurnal variations and wind speed) and initial conditions (e.g. depth to water table) were varied in each experiment. Numerical results were compared with experimental data in the absence of empirically defined enhanced vapor diffusion. The different formulations showed varying degrees of ability to accurately predict evaporation/condensation rates. The modified HK formulation best preserved the shape of the evaporation curves during stage 1 and 2 evaporation. The other four formulations greatly overestimated/underestimated stage 1 evaporation and underestimated stage 2 evaporation. In addition to providing the best evaporation estimates, the HK formulation did not require the use of empirical fitting parameters. Comparisons of the various formulations demonstrate the importance of capturing the correct physics at the land-atmospheric interface in order to estimate evaporation/condensation. Accounting for phase change is applicable to current hydrologic and environmental problems including land-atmospheric modeling and understanding contaminant volatilization and transport in the shallow subsurface.