Physically Based Thermodynamic Model of the Water Retention Curve of Soils for the Entire Water Range

Abstract

Quantitative description of the water retention curve (WRC) of soils remains one of the most pressing problems in hydrophysics due to its importance for computer modeling of the transport of soil water and dissolved substances, as well as for the development of the thermodynamic concept of soil physical properties. A new WRC model is presented as a functional dependence of the thermodynamic potential (pressure) of water and its content in the soil over the entire possible range from conditionally zero water content to the maximum water holding capacity. Unlike well-known empirical analogues, the model is based on fundamental physical mechanisms of water retention, combining the capillary effect and disjoining water pressure (according to Derjaguin). Limitations by porosity (maximum water holding capacity), the height of the limiting capillary rise, and the standard thermodynamic potential of conditionally zero water content at a temperature of 105°C are used to justify the domain of determination of the WRC, its inflection point, and scaling. The analytical expression of the new model as a combination of exponential and hyperbolic functions with the argument of soil water content is easily differentiated and allows to calculate, using the WRC, the differential water capacity, variable phase interface, and pore size distribution with a maximum value of field capacity, and to estimate the specific surface area of the solid phase. Validation of the model using mean statistical WRCs of the main genetic types and textural classes of some soils in Eurasia confirms its good agreement with experimental data with a more adequate description of WRC in the vicinity of conditionally zero soil water content compared to the standard empirical van Genuchten’s model with the same number of parameters. The fundamental nature of the new model and its good approximation ability for the entire range of WRC create the prospect of its diverse use for assessing the physical quality of soils and process modeling of water transfer, especially in finely dispersed and highly drying arid soils, where the approximating capabilities of the model exceed the known empirical analogues.