Hydrostatics and Hydrodynamics in Swelling Media

The point of departure is hydrodynamics in unsaturated non-swelling media, particularly the “diffusion analysis” developed in mathematical soil physics. Generalisations of this approach to two- and three-component horizontal systems in swelling media are described. The generalization to vertical systems demands reconsideration of hydrostatics in swelling media. The total potential includes, in this case, an additional component, the overburden potential , Ω, Evaluation of Ω leads to the condition for equilibrium in the vertical. This reduces to a first-order linear diff. eqn. with singular coefficients. It follows that there are three types of equilibrium profile: hydric profiles with the moisture gradient dθ/dz pycnotatic profiles with dθ/dz = 0; and xeric profiles with dθ/dz > 0. Both hydric and xeric profiles approach the pycnotatic state (of maximum apparent specific gravity) in depth. Classical concepts of groundwater hydrology (tacitly based on the behaviour of non-swelling media) fail completely for swelling media. The steady vertical flow equation in swelling systems reduces to a second-order linear d.e. with singular coefficients. The, somewhat complicated, set of possible flows is established. These include upward flows against the moisture gradient. The non-steady vertical flow equation is derived. It is shown how its solution leads to the theory of one-dimensional infiltration in swelling media.