Development of Mathematical Model of Heat and Mass Transfer in Soil, with Provision for the Gradients of soil-water and soil-salt potentials. Part 2

摘要

The article is devoted to mathematical modeling of heat and mass transfer in soil. The construction of different structures on heaving soils requires verification of their stiffness. Frost heaving comes with water displacement from the thawed to freezing soil and ice segregation. This process is only possible in a non-equilibrium conditions. To describe the movement patterns of interstitial solution, most scientists use the generalized thermodynamic laws based on the action of all the thermodynamic driving forces. Without the using of non-equilibrium thermodynamics laws, this approach does not allow to identify the link between kinetic coefficient determined by different mechanisms. In the first part of this article, the authors proved that the potential of all components of water-salt solution in soil may consist of the chemical potential and the potential of external volume forces, which are non-zero. Also in the first part the authors derived the equation of the dynamics of pore solution, which takes into account the gradients of decreasing the potential of all components of solution in soils. In second part of the article, the authors used the equation of pore solution dynamics and the conclusions of the first part to develop a mathematical model of heat and mass transfer in soils. The equation of the speed of changing of kinetic energy, potential energy, sorption energy, internal energy and total energy conservation, potential energy conservation and total energy was written. With the help of the second law of thermodynamics, the equation for the transfer of entropy is written. Onsager theorem and volume source of entropy allowed to write the equations for thermodynamic driving forces and flows with allowance for cross effects.