Solute rejection in freezing soils

Dissolved compounds in the water phase are rejected during freezing of soils. This phenomenon occurs due to the inability of ice crystals to incorporate most alien molecules. The ice grows only by association with water molecules, and molecules of solutes are rejected into the unfrozen water. A mathematical model for salt rejection in freezing saline soils has been developed by employing the mass balance equations for water and solute in a saturated porous medium, and the conservation of energy equation. Additional relations introduced include a moisture retention curve as a function of ice‐water capillary pressure, the Clapeyron equation and expressions for the heat capacity and the effective thermal conductivity of the soil. The resulting set of seven equations in terms of solute concentration, soil temperature, pore water, ice, and capillary pressures, and degrees of water and ice saturation have been solved simultaneously using a Newton‐Raphson linearization, with implicit iterative treatment of nonlinearities. Results indicate the development of unfrozen high salt concentration regions trapped in a frozen zone at sufficiently high freezing rates. The numerical results are compared with experimental data obtained by some researchers. Favorable match is obtained between the theoretical and experimental results. Finally, extension of the model to situations where ice lensing and soil deformations are significant is discussed.