An analytical model for evaporation from unsaturated soil

Abstract

Evaporation from unsaturated soil is characterized by vapor transfer in the upper part and liquid water transfer in the lower part of the soil. This study develops an analytical model for identifying the vaporization plane where the evaporation occurs, and the model consists of three partial differential equations that respectively govern the vapor flow, liquid water flow and heat transfer. These equations are solved simultaneously for the transient water content profile, evaporation rate, transient temperature profile and location of the vaporization plane. A series of experiments are used to validate the proposed analytical model, which indicates that this model can reasonably well predict the temporal water content profile and evaporation rate during the evaporation process. The result shows that the evaporation rate during falling rate stage is proportional to the inverse of the square root of elapsed time, and the proportionality is affected by the vapor diffusion coefficient, heat diffusion coefficient, and critical water content. The depth of vaporization plane is found to be independent of soil hydraulic properties, but only dependent on the heat diffusion coefficient of the soil. It is also revealed that heat diffusion coefficient has a pronounced influence on the evaporation process, which has not been observed in previous studies. A larger thermal diffusion coefficient leads to a faster advancing and a deeper vaporization plane, as well as a faster decreasing evaporation rate. The analytical model provides a useful tool for investigating the mechanism of the evaporation process.