Solute transport in the subsurface is often considered to be a nonequilibrium process. Predictive models for nonequilibrium transport may be based either on chemical considerations by assuming the presence of a kinetic sorption process, or on physical considerations by assuming two‐region (dual‐porosity) type formulations which partition the liquid phase into mobile and immobile regions. For certain simplifying conditions, including steady state flow and linear sorption, the chemical and physical nonequilibrium transport models can be cast in the same dimensionless form. This paper presents a comprehensive set of analytical solutions for one‐dimensional nonequilibrium solute transport through semi‐infinite soil systems. The models involve the one‐site, two‐site, and two‐region transport models, and include provisions for first‐order decay and zero‐order production. General solutions are derived for the volume‐averaged (or resident) solute concentration using Laplace transforms assuming both first‐ and third‐type inlet conditions, and arbitrary initial conditions, input solute concentrations, and solute production profiles. The solutions extend and generalize existing solutions for equilibrium and nonequilibrium solute transport. The general solutions are evaluated for some commonly used input and initial conditions, and zero‐order production profiles. Expressions for the flux‐averaged concentration are derived from the general and specific solutions assuming a third‐type inlet condition. Typical examples of calculated concentration distributions resulting from several sets of initial and input conditions and zero‐order production functions are also presented and briefly discussed.

The diffusion of warm, humid air into an initially cold, dry, sandy column was analyzed to study the movement of water vapor and liquid water under nonisothermal and low water content conditions. The analysis was performed using the HYDRUS‐1D code. While the water retention curve of sand was measured experimentally, the unsaturated hydraulic conductivity function was inversely estimated from the observed water content profiles in the column. The estimated unsaturated hydraulic conductivity function displayed a shape that reflected distinct processes of capillary pore water flow and film flow at high and low water contents, respectively. Four components of the total water flux, including thermal and isothermal liquid water and water vapor fluxes, were evaluated using the calibrated soil hydraulic properties. Evaporation and condensation rates were calculated based on water mass balance. Water vapor entered the soil column at the hot surface and condensed at the cold bottom. Subsequently, liquid water moved upward and evaporated at the moisture front in the middle of the column where the relative humidity decreased below unity. Liquid water and water vapor then circulated between the bottom and the moisture front, accompanied by condensation and evaporation processes. The impact of the enhancement factor in the thermal vapor diffusion term could not be clearly identified from available experimental water content profiles. Increases in liquid water flow and the evaporation rate could be compensated for by increases in vapor flow and the condensation rate. Additional data would be needed to fully evaluate the effect of the enhancement factor.

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