Water present in an unsaturated porous medium such as soil is subject to a variety of forces acting in different directions. The terrestrial gravitational field and the overburden loads due to the weight of soil layers overlying a nonrigid porous system tend to move the soil water in the vertical direction. The attractive forces occurring between the polar water molecules and the surface of the solid matrix and those coming into play at the separation interface between the liquid and gaseous phases can act in various directions. Moreover, ions in the soil solution give rise to attractive forces that oppose the movement of water in the soil.
Because of difficulties in describing such a complex system of forces and because of the low-velocity flow field within the pores, so that the kinetic energy can be neglected, flow processes in soil are referred instead to the potential energy of a unit quantity of water resulting from the force field. Thus, flow is driven by differences in potential energy, and soil water moves from regions of higher to regions of lower potential. In particular, soil water is at equilibrium condition if potential energy is constant throughout the system.
Because only differences in potential energy between two different locations have a physical sense, it is not necessary to evaluate soil water potentials through an absolute scale of energy, but rather they are referred to a standard reference state. This standard reference state usually is considered as the energy of the unit quantity of pure water (no solutes), free (contained in a hypothetical reservoir and subject to the force of gravity only), at atmospheric pressure, at the same temperature of water in the soil (or at a different, specified temperature), and at a fixed reference elevation. The concept of soil water potential is of fundamental importance for studies of transport processes in soil and provides a unified way of evaluating the energy state of water within the soil-plant-atmosphere system. To consider the different field forces acting upon soil water separately, the potential is used, defined thermodynamically as the difference in free energy between soil water and water at the reference condition.
A committee of the International Soil Science Society  defined the total soil water potential as "the amount of work that must be done per unit quantity of pure water in order to transport reversibly and isothermally an infinitesimal quantity of water from a pool of pure water at a specified elevation at atmospheric pressure to the soil water (at the point under consideration)." This definition, though a really formal one and not useful for effectively making measurements [7, 8], allows us to consider the total potential as the sum of separate components, each of which refers to an isothermic and reversible transformation that partly changes water state from the reference condition to a final condition in the soil.
Following the Committee's proposal, the total potential of soil water, ft, can be broken down as follows:
where the subscripts g, p, and a refer to the gravitational potential, the pressure potential, and the osmotic potential, respectively. Different units can be employed for the soil water potentials and they are reported under "Units of Potential," below.
The potentials fg and fa account for the effects of elevation differences and dissolved solutes on the energy state of water. The pressure potential f p comprises all the remaining forces acting upon soil water and accounts for the effects of binding to the solid matrix, the curvature of air-water menisci, the weight of overlying materials, the gas-phase pressure, and the hydrostatic pressure potential if the soil is saturated. Thus, strictly speaking, the gravitational and pressure potentials refer to the soil solution, whereas the osmotic potential refers to the water component only.
However, the above definition of pressure potential fp generally is not used because, in the realm of soil physics, the energy changes associated with the soil water transport from the standard reference state to a certain state in the soil at a fixed location are traditionally split up into other components of potential that separately account for the effects of pressure in the gaseous phase, overburdens, hydrostatic pressure, and links between water and the solid matrix.
The component of pressure potential that accounts for adsorption and capillary forces arising from the affinity of water to the soil matrix is termed matric potential fm. Under fully saturated conditions, fm = 0. In nonswelling soils (for which the solid matrix is rigid) bearing the weight of overlying porous materials and in the presence of an interconnected gaseous phase at atmospheric pressure, the matric potential fm coincides with pressure potential ^p. Under relatively wet conditions, in which capillary forces predominate, the matric component of the pressure potential can be expressed by the capillary equation written in terms of the radius of a cylindrical capillary tube, Reff (effective radius of the meniscus, in meters):
where Pc = Pnw - Pw is the capillary pressure (N/m2), defined as the pressure difference between the nonwetting and the wetting fluid phases, a is the interfacial tension between wetting and nonwetting fluid phases (N/m), and ac is the contact angle. If the nonwetting phase is air at atmospheric pressure, the capillary pressure is equal to - .
Moreover, the sum of the matric and osmotic potentials often has been termed water potential ^w, and it provides a measure of the hydration state of plants, as well as affecting the magnitude of water uptake by plant roots.
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