In seasonally frozen soils, liquid water will, for all practical purposes, always be present. The liquid films in frozen soils are the transport corridors for water and solutes. Transport processes in porous media, in which gradients of temperature, water potential and salt concentration occur simultaneously, are best described by the theory of non-equilibrium thermodynamics. This branch of science is well developed. It presents an elegant framework for the description of all primary transport processes and all coupling phenomena, and offers a symmetric matrix of transport coefficients in agreement with the theory of Onsager.
The extensive and intensive variables, including the liquid pressure, the ice pressure, and the load (overburden) pressure, which are involved in the development of this theoretical framework, are related by ratios of partial differentials, the so called Maxwell relations. They are derived from the total differential of a certain expression of the free energy of the system. Beside the well-known Helmholtz and Gibbs free energies, there are many more possible choices of expression of the free energy of a system. For a frozen system containing soil, water, ice, air, and one single solute, there are some twenty nine additional choices. Each choice of free energy leads to some fifteen Maxwell relations, for a total of four hundred sixty five. Most of these relations are pretty useless. Some of them, however, are real gems.
One of the Maxwell relations, relating the ratio of the partial differentials of the osmotic pressure and the load pressure to the ratio of the partial differentials of the void ratio and the "Lagrangian" solute concentration, will be discussed, and its implications concerning the effect of application of solutes, such as fertilizers and road salt, to frozen soil on the heaving pressure, will be explored.
Pieter H. Groenevelt Dept. of Land REsource Science University of Guelph Guelph, Ontario N1G 2W1 CANADA Phone: (519) 824-4120 x3585 Fax: (519) 824-5730 E-mail: pgroenev@lrs.uoguelph.ca