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The Theory Of Philip And De Vries

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(Saito, Simunek, & Mohanty, 2006)
Early pioneering studies on interactions between liquid water, water vapour, and heat movement were reported by Philip and de Vries (1957), who provided a mathematical description of liquid water and water vapour fluxes in soils driven by both pressure head (isothermal) and soil temperature (thermal) gradients.
They derived the governing flow equation for non-isothermal flow as an extension of the Richards equation, which originally considered only the pressure head gradient. The theory of Philip and de Vries (1957) was later extended by Nassar and Horton (1989), who additionally considered the effect of an osmotic potential gradient on the simultaneous movement of water, solute, and heat in soils.
Heat transport and water flow are coupled by the movement of water vapour, which can account for significant transfer of latent energy of vaporization. Soil temperatures may be significantly underestimated when the movement of energy associated with vapour transport is not considered. For example, Cahill and Parlange (1998) reported that 40 to 60% of the heat flux in the top 2 cm of a bare field soil of Yolo silt loam was due to water vapour flow. Fourier?s law describing heat transport due to conduction (e.g., Campbell, 1985) thus needs to be extended to include heat transport by liquid water and water vapour flow. The general heat transport model then considers movement of soil heat by (i) conduction, (ii) convection of sensible heat by liquid

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