Water transfer and ice formation in soils
2.1 Nature and mechanism of moisture migration in soils
Water migration in unsaturated soils is due to a complex mass transfer mechanism and a variety of water exchange driving forces. For geocryological problems the most interesting is the migration of bound and capillary water and vapour. Seepage (movement of free or gravitational water) in finegrained materials is of minor significance and will not be discussed further. Water migration and vapour transfer in soils are related to the solution of many problems in earth science, engineering geology, pedology and geocryology (absorption and evaporation of water from the soil surface, its resorption by surrounding soil layers, capillary replenishment of soil, water migration towards the front of freezing and cooling, etc.). Thermodynamically, water and vapour migration in soil follow from the disequilibrium of the soilwater system caused by change in time and space of thermodynamic parameters (temperature, pressure, ion concentration, humidity, electrical, magnetic and gravitational potentials, etc.). It is usually impossible to measure directly the driving force of each mechanism separately. This is the reason to find a uniform (generalized) force comprising more or less fully all component forces. All this has resulted in an energy (thermodynamic) approach to mass transfer in colloidal and capillary porous bodies including the soil system.
All the water in soils, with the exception of free (gravitational) water, is held due to the free surface energy of the mineral soil skeleton Es. Under the interaction of minerals with water, or more precisely, with a water solution, a part, £w, of this energy is attributable to the bonding of ions of double electrical layers to water molecules. The difference Es — £w = Eu is the part of the surface free energy of the soil system not spent on the interaction with water solution. Evidently the basic driving force of water transfer in the liquid phase (i.e. water migration in soil) is the gradient of this energy, Eu. This is a value of specific Gibbs free energy often called the absolute chemical or isobaricisothermal potential of bound water p!i0. Because the absolute values of many thermodynamic functions, /.i'(0 included, are not measurable, what is sought is not the absolute, but the relative thermodynamic potential of bound water: n(0 = ¡.i'm — /¿0, where p.0 is the absolute chemical potential for free water. Since ¡.i'm< ¡.i0, fi0} is a negative value.
The relative thermodynamic potential of soil water represents comprehensively the free energy reduction of free water when it interacts with a solid body. It is the work done in reversibly and isothermally converting 1 g of free water into bound water. Moisture potential, characterizing the energy of bound water in soil, is measured in units of work with respect to a unit of water mass (e.g. J kg ~1, J mol ~1 etc.).
The thermodynamic potential of soil moisture is a sum of particular potentials
Va> = ^co + «Ac + <AZ + <Ap + «Ae + «Am + ••• (2.1)
where i/zjis the matrix (capillaryadsorption) potential, i.e. the work spent on conversion of unit water mass from a solution, identical with that of the soil, to bound water (this potential comprises sorption and meniscus phenomena); ij/0 is the osmotic potential, i.e. the work spent on transference of unit of water mass from a volume of pure water to a volume containing a solution identical in composition and structure with that of the soil; ij/z is the gravitational potential, i.e. the work needed to transfer a solution, similar to that of soil, from one elevation to another; i]/ is the hydrostatic (or external gas pressure) potential expressing the work done on the soil due to the action of external pressure; and ij/e, ij/m are the electrical and magnetic water potentials respectively.
Note that a rise in temperature results in a higher water potential. This is associated with the increasing translatory movement of water molecules and a reduction in the energy of bonding with the soil matrix. Because the potential is characterized by a negative value, its algebraic value rises while its absolute quantity diminishes.
The soilwater potential ¡.im depends on the soilwater content Wvol (gem3). By analogy with volumetric heat capacity for a temperature field, A.V. Lykov has introduced the notion of volumetric isothermal mass capacity or differential soilwater capacity Cm showing how much water is to be added to the soil to change the water potential by a unit amount. It is a variable which depends on the soilwater potential, and on the composition, structural and mechanical characteristics of the soil and it is calculated from the relation:
Fig. 2.1. Dependence of moisture potential and volumetric differential moisture capacity Cm (dashed line in a), and (in b) hydraulic conductivity coefficient of ground water /tmand diffusion coefficient K01, on water content of soils: 12  claysilty sand (1  light; 2  heavy); 3  medium silty sand; 4  clay; 5 kaolinite clay; 6  hydrous mica montmorillonite clay with pd = 1.56gem*3.
Fig. 2.1. Dependence of moisture potential and volumetric differential moisture capacity Cm (dashed line in a), and (in b) hydraulic conductivity coefficient of ground water /tmand diffusion coefficient K01, on water content of soils: 12  claysilty sand (1  light; 2  heavy); 3  medium silty sand; 4  clay; 5 kaolinite clay; 6  hydrous mica montmorillonite clay with pd = 1.56gem*3.
where T is the absolute temperature. Soilwater potential and differential soilwater capacity can vary by one or two orders of magnitude (Fig. 2.1a).
Relating to water potential is the notion, introduced by B.Y. Deryagin, of wedging pressure of thin films of bound water Pwed which is the pressure difference observed in crossing the flat interface surface from the bound water, present in a thin layer, to the adjacent water, and equal to:
where Vm is the molar volume of water; and /¿^ are the full thermodynamic potentials of the ground water and filmbound water respectively; A and m are coefficients representing characteristics of the mineral surface and water solution respectively; h is the thickness of the bound water films between two soil particles. The value of Pwed is negative.
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