Border-line cases of the water vapor sorption model of the soils with source-drainage function

Abstract

   A theoretical analysis of the influence of the source-drain on the dynamics of the sorption process for one particular (border-line) case is given for the non-classical mathematical model of the process of water vapor sorption by the soil surface with a source-drain developed by the authors. Unlike the model of M. Griesmer, in which the sorption equation is homogeneous, in the proposed model the sorption equation is heterogeneous – there is a constant non-zero free term, which is considered as a parameter of external influence on the system (source-drain function). The parameter allows controlling the sorption process by changing its characteristics. The solution of the model equation determines the basic analytical relationship for analyzing the dynamics of soil volumetric water content as a function of time. The behavior of the volumetric water content function is determined by the influence of the selected parameter value as well as by the relationship between constant initial and equilibrium moisture, for which three variants are possible. As a result of studying the dynamics of soil system volumetric moisture according to the developed model, it has been established that in this case the sorption process will proceed in three modes: the first mode of the modeled process is a time-limited, finite process of critical soil drying; the second mode is a stationary process, when soil volumetric water content does not change over time and remains equal to the initial moisture (the process asymptotically degenerates); in the third case, the considered sorption model describes a time-unlimited asymptotic process of soil volumetric water content fall from the initial value to the limiting (non-zero) value.