Linear Equations for the Simultaneous Flow of Matter and Energy in a Continuous Soil System

Abstract

Some transfer processes in soil are considered with respect to recent developments in the theory of thermodynamics of irreversible processes. The theory provides a general and systematic guide for setting up interrelated equations describing the transport of one or more components through soil. Darcy's law and the "diffusion equation" are shown to be components of this general development. Particular attention is given to the nonisothermal flow of moisture and energy through soil. A general relation between the fluxes induced by the combined gradients of moisture content, temperature, and solutes is also suggested.

Soil Moisture Transport Due to Thermal Gradients: Practical Aspects

“…As the soil's gas phase expands and contracts under the KQ dT a T dz [21 (2) where the symbols are defined in the appendix. While equations [1] and [2] were developed primarily from the general theory of irreversible thermodynamics, Taylor and Cary (21) have shown that these equations are identical in form to the equations developed by Philip and de Vries (16). In fact, most investigators have used similar relations.…”

The Dynamics of Soil Water: Part II-Temperature and Solute Effects

“…Since the creation of entropy .is a time and rate dependent quantity, it seems reasonable to suppose that the natural transport of mass and energy in the soil system will occur simultaneously in a way such that the entropy proceeds toward a maximum. Based on this philosophy and certain assumptions (Taylor and Cary, 1964), it can be argued that the flux of water in the soil may be described by n d…”

Modelling soil water dynamics in the unsaturated zone -state of the art

“…The thermodynamic approach involves the use of thermodynamica of irreversible processes tagether with the Clapeyron equations to derive the coupling coefficients (TAYLOR and CARY, 1964). BOLTand GROENEVELT (1972) and KAY and GROENEVELT (1974) give a derfvation of the basic partlal differential equations for the case, when matric potentlal is considered as a superficial driving force.…”