Table 1. Matrix of direct and coupled transport phenomena in frozen porous media

Workman Reynolds Effect (Drost-Hansen 1967,

view, I want specifically to examine the roles of

Murphy 1970, Hanley and Rao 1982). Freezing po-

soil chemical properties on moisture movement in

tentials are properties of dilute solutions and pure

freezing and frozen soils. Before discussing chemi-

water and disappear at high concentrations (Drost-

cal effects, however, we need a theoretical frame-

Hansen 1967, Murphy 1970). Although Hanley

work for the discussion.

and Rao (1982) developed a model to quantify the

Following Perfect et al. (1991), we will use the

relation between freezing potentials and the mi-

nonequilibrium thermodynamic approach, where

gration of moisture and ions in freezing soil, the

fluxes are written as explicit functions of both

overall significance of this phenomenon for soil

direct and coupled transport phenomena. For ex-

freezing is unclear. Another electrical phenome-

ample,

non, electro-osmosis, can cause considerable wa-

jw = -Lwh∇T /T - Lww∇pl

ter movement, but this is only important in cases

where induced electrical potentials are applied to

(6)

soils (Hoekstra and Chamberlain 1964). Outcalt et

- Lws∇π - Lwe ∇ ε

al. (1989) monitored electric potentials in freezing

soils during diurnal and seasonal freezethaw

js = -Lsh∇T /T - Lsw∇pl

cycles. They concluded that the rapid and system-

(7)

atic pattern of electrical potential variation dur-

- Lss∇π - Lsc∇ε

ing freezethaw events demonstrates that the

effects of electrolyte concentration and dilution are

products of evaporationdistillation, melting of

where

jw and js = fluxes of liquid water and

frost-purified ice, soil water advection to the freez-

solute

∇T, ∇pl, ∇π and ∇ε = gradients in temperature,

ing region, electrolyte expulsion from the freez-

ing region and infiltration of rain and snowmelt.

hydrostatic pressure, solute

They further concluded that soil electrical poten-

concentration and charge

tials will yield valuable information concerning

Lmn = transport coefficient relating

the mth flux (jm) to the nth

the state and mobility of soil water in freezing and

thawing soils.

component.

In general, water moves from warm to cold,

from regions of low solute concentration to high-

Fluxes and their driving forces (gradients) in fro-

solute regions and from high-moisture zones to

zen porous media are summarized in Table 1.

low-moisture zones (Perfect et al. 1991). Chemical

Water moves in soil (jw) in response to changes

potentials of water due to gradients of hydrostat-

in the chemical potential of water, which is related

to gradients in the hydrostatic pressure (∇pl) (Dar-

ic pressure, solute concentration and temperature

interact additively to create a strong thermody-

cy's Law), temperature (thermo-osmosis), solute

namic sink for liquid water at the freezing front

concentration (capillary osmosis) and electrical

(Fig. 3). As soils freeze from the top downward,

potential (electro-osmosis) (Table 1, eq 6).

the thermal gradient will induce an upward flow

At the freezing front in dilute solutions, anions

of water to the freezing front. Solutes are largely

(generally) are preferentially absorbed into the ice

excluded in the freezing process, and maximum

phase, leading to a measurable charge separation

solute concentrations are generally found imme-

(freezing potentials); this phenomenon is called the

Table 1. Matrix of direct and coupled transport phenomena in frozen

porous media. (After Perfect et al. 1991).

Driving force

∇T

∇pl

∇π

∇ε

Flux

[Dufour Effect]†

FOURIER'S LAW*

Thermofiltration

Peltier Effect

Thermo-osmosis

Capillary osmosis

Electro-osmosis

DARCY'S LAW

Soret Effect

Reverse osmosis

[Electrophoresis]

FICK'S LAW

[Seebeck Effect]

Streaming potential

[Diffusion potential]

OHM'S LAW

* Direct processes are upper case; coupled processes are lower case.

† No reference to bracketed processes found in the soil freezing literature.