A Comparison of Two Theoretical Models for Calculating Water Flux under Non-isothermal Conditions

Using the data on water content and temperature distribution in uniformly packed 10 cm long closed horizontal soil columns wetted to θ₀=0.075, 0.184 and 0.28 cm³ cm⁻³ and subjected to ∇ T=0.5 and 1°C cm⁺¹, the flux of water was calculated from Philip-de Vries and Taylor-Cary theories. The values of transport coefficients were calculated for every cm interval along the soil column using the transient water content and steady temperature data. The isothermal and thermal liquid diffusivities increased and the isothermal and thermal vapour diffusivities decreased with increase in water content. The transfer coefficient β varied with water content and temperature of every cm interval along the column. Both the theories predict that at 0.28 cm³ cm⁻³ the moisture content gradients created due to thermally induced water flow caused greater flux of water from cold to hot side than that from hot to cold side. The magnitude of this effect was shown more by Taylor and Cary theory than by Philip and de Vries theory. At 0.075 cm³ cm⁻³ the Philip and de Vries theory predicated net water flux reasonably close to observed values for 0.36 h interval where the Taylor and Cary theory yielded negative values.

The reverse was true for 76–150 h interval where the Taylor and Cary theory predicted close to observed flux and the Philip and de Vries theory over-predicted by 14 to 23 times. The range of water content in which both the theories were found suitable varied from 0.075 to 0.184 cm³ cm⁻³.