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The soil gas and solute diffusion coefficients and their dependency on soil total porosity (Φ), fluid-phase (air or water) contents, and pore-size distribution largely control chemical release, transport, and fate in soil. The diffusion coefficients hereby play a key role in both local and global environmental issues including spreading, biodegradation and volatilization of hazardous chemicals at polluted soil sites, and soil uptake, production, and emission of greenhouse gases. In a series of papers, we present new advances in describing and predicting the gas and solute diffusion coefficients in variably saturated porous media, carefully distinguishing between repacked and undisturbed media. Also, we establish direct links between gas and solute diffusivity and pore-size distribution, with further links to pore continuity and tortuosity. In this first paper, a porosity correction term is added to a recently presented model for predicting gas diffusivity in repacked soil. The obtained POrosity-Enhanced (POE) model assumes that increased Φ creates additional interconnectivity between air-filled pores. The POE model is tested against data for 18 repacked soils ranging from 0 to 54% clay, including new data measured in this study for both noncompacted and compacted, high-porosity soils. The POE model accurately predicts gas diffusivity across a wide Φ range up to 0.75 m3 m -3 , whereas the original model is accurate only for Φ up to 0.55 m 3 m -3 . A unifying, two-parameter function for gaseous phase pore continuity (f g ) is suggested. The f g function illustrates developments in gas diffusivity models during the last century, including assumptions behind the increasingly precise prediction models for repacked soil. Last, the POE model is coupled with the widely used van Genuchten (vG) soil-water characteristic model, hereby establishing an accurate and predictive link between soil gas diffusivity and pore-size distribution. The closed-form POE-vG gas diffusivity model is highly useful to evaluate effects of pore-size distribution and soil type on gas diffusivity and gas transport in repacked soil systems.

Accurate description of the soil-gas diffusion coefficient (Dp) as a function of air-filled (e) and total (Φ) porosities is required for studies of gas transport and fate processes. After presenting predictive models for Dp in repacked and undisturbed soils (Part I and II), this third paper takes a more descriptive approach allowing for the inclusion of inactive air-filled pore space, e in . Three model-based interpretations of e in are presented: (1) a simple power-law model (labeled Millington-Call) with the exponent (V) taken from Millington (1959; Science 130:100-102), and expanded with a constant e in term (= 0.1 m 3 m -3 ), (2) a model (SOLA) based on analogy with solute diffusion and assuming a linear increase in pore continuity from zero at the threshold air-filled porosity where gas diffusion ceases (e th ) to a maximum at e = Φ, (3) a power-law model (VIPS) assuming variable e in that linearly decreases from a maximum at e = e th to zero at e = Φ. Assuming e th = 0.1 m 3 m -3 , all three models satisfactorily predicted Dp in 18 repacked soils. The difference between the three models is mainly pronounced for higher-Φ soils, and each model has its own advantage. The SOLA model together with similar models for solute diffusivity allows a direct comparison of pore continuity in the soil gaseous and liquid phases, suggesting large differences in tortuosity and inactive fluid-phase between the two phases. The low-parameter Millington-Call model could account for variability in measured Dp along a field transect (Yolo, California) by varying e in with ±0.03 m 3 m -3 3 and is applicable for stochastic gas transport simulations at field scale. The mathematically flexible VIPS model highly accurately fitted D P (e) data for undisturbed soil, illustrating the large possible variations in e th and V. The VIPS model is coupled with the van Genuchten (vG) soil-water characteristic model, yielding a closed-form expression for Dp as a function of soil-water matric potential. The VIPS-vG model is useful to illustrate the combined effects of pore size distribution and inactive pore space on soil-gas diffusivity.

Solute diffusivity (ratio of diffusion coefficients in soil and free water, D s /D 0 ) is markedly soil-type dependent. Soil texture and pore size distribution govern the threshold soil-water content (θ th ) where D S /D 0 approaches zero as a result of discontinuous diffusion pathways. In a recent study (Soil Science 161:633-645), we suggested that θ th can be predicted from the soil-water characteristic curve (SWC) based on the Campbell pore size distribution parameter, b. In this study, the θ th -b expression was recalibrated based on diffusivity data for three soils (Hiroshima sand, Foulum loamy sand, and Yolo loam) measured in this study plus 20 soils reported in the literature, obtaining θ th =0.020b. As the SWC is often not measured, a second θ th expression that requires only knowledge of soil texture and bulk density was calibrated from measured data. A third expression, including both soil texture, bulk density, and Campbell b, was also calibrated and gave the most accurate description of θ th . The solute impedance factor (ratio of diffusivity by volumetric soil-water content), f 1 = D S /(θ Do), was shown to increase linearly with the water content available for diffusion, θ a =θ - θ th . The slopes of the f 1 -θ a relations were similar for most soils and did not exhibit soil-type dependency. Based on this, a so-called constant slope impedance factor (CSIF) model to predict D S (θ a )/D 0 is presented. The model can be used in combination with any of the three suggested θ th expressions. Combined with the soil-texture/bulk-density dependent θ th expression, the model accurately predicted solute diffusivities for three independent soils for which the SWC were not known.

Predictive models for the solute diffusion coefficient, D S , dependency on volumetric soil-water content, 0, are often applied in simulations of solute transport and fate in natural, undisturbed soils. However, all available D S (θ) models have been developed from measurements on sieved, repacked soil. In this study, D S for chloride was measured in both repacked and undisturbed loamy sands at different soil-water contents. The measurements on undisturbed soil were carried out using a modified half-cell method, where the source half-cell is a sieved and repacked soil core and the other half-cell is an undisturbed soil core. Thus, the problems of (i) incomplete contact area at the interface between undisturbed half-cells and (ii) potentially different diffusion properties in undisturbed half-cells can be avoided. The modified half-cell method requires that the diffusion coefficient in sieved, repacked soil is determined separately and that the experimental data is analyzed with a numerical solution to the diffusion equation. No significant difference in chloride D S (θ) between undisturbed and sieved, repacked soil was observed for a Danish (Foulum) loamy sand and a Japanese (Hiroshima) loamy sand. A recently presented soil type dependent D S (θ) model, derived from repacked soil data, shows it to be applicable also for predicting solute diffusion coefficients in natural, undisturbed soils.

Investigations of gas transport and fate processes in packed soil systems require knowledge of the gas diffusion coefficient, D p , as a function of air-filled porosity, e. On the basis of the literature, data from six studies over the porosity range of 0.1 to nearly 1.0, it is reconfirmed that the Marshall (1959) model better predicts D p (e) in completely dry, repacked porous media than do the Penman (1940) and Millington (1959) models. The smaller D p value in wet soil, as compared with dry soil at the same air-filled porosity, is accounted for by introducing a water-induced linear reduction (WLR) term, equal to the ratio of air-filled porosity to total porosity, in the D p (e) model. By adding the WLR term in each of the three D p (e) models for dry porous media, the so-called WLR(Marshall), WLR(Penman), and WLR(Millington) D p (e) models for wet soil are developed. To test the three WLR models, D p was measured at different soil-water contents in six differently textured (6-38% clay) repacked soils. The WLR (Marshall) model accurately and best described D p (e) for all six soils and additional soils from the literature. All three WLR models performed better than previous D p (e) models. This study implies that the smaller D p in a wet soil, which is due to water-induced changes in air-filled pore shape and pore connectivity, can be described by a simple, linear function of relative air-filled porosity. The WLR(Marshall) model represents a conceptual and accurate model to predict D p (e) in sieved, repacked soil.

Diffusion of hydrophobic organic compounds (HOC) is a key process controlling transport of contaminants in soils. However, the separate effects of sorption and diffusion on net (effective) HOC diffusion are not fully understood. In this study, effective diffusion of naphthalene in five unsaturated soils was evaluated by: (i) naphthalene adsorption-desorption experiments (batch method), (ii) naphthalene effective diffusion experiments (half-cell method), and (iii) trace-gas diffusivity experiments (chamber method). There was no soil type effect on gas diffusivity in repacked unsaturated soil, but a pronounced soil type effect on naphthalene sorption behavior. Varying degree of adsorption nonlinearity (Freundlich n' a ) and apparent adsorption-desorption nonsingularity (ω) and w increased with decreasing n' a were observed. In the half-cell experiments, gas diffusion was the governing naphthalene transport mechanism. Three effective diffusion coefficients were calculated from the half-cell experiments, based on concentration profile from either the whole (D eff ) cell, the source (desorption) half-cell (D eff,D ), or the recipient (adsorption) half-cell (D eff,A ). Generally, the observed D eff decreased with naphthalene-soil contact time, because of aging effects. The D eff , D eff,A , and D eff,D values (half-cell method) could only to some extend be estimated from Freundlich isotherm parameters (batch method). A suggested index of effective diffusion nonsingularity, H = D eff,D /D eff,A , showed that H was correlated with w and inversely correlated with n' a . Thus, the sorption nonlinearity (n' s ) was found to provide good indications of degree of nonsingularity in both HOC adsorption-desorption and effective diffusion. The combination of batch and half-cell experiments generally gave useful insight towards understanding and predicting the influence of sorption nonlinearity and nonequilibrium on HOC diffusion.

Diffusion processes in the soil water and air phases often govern transport and fate of nutrients, pesticides, and toxic chemicals in the vadose zone. This final paper in a 10-part series on diffusion-reaction processes in soils concerns the development of a unifying model platform for predicting so

Transport models for sorbing organic chemicals in soil require accurate predictions of the diffusion and sorption processes in both the liquid and gaseous phases. In this study, the ability of recently-presented diffusivity models in combination with equilibrium sorption models to predict the effective (i.e., including sorption effects) diffusion coefficient, D eff , as a function of soil-water content, θ, is tested for different sorbing organic chemicals in different soils. The water-induced linear reduction (WLR) gas diffusivity model, combined with a two-component (hydrophobic and vapor) equilibrium sorption model, well described short-term ( 700 h. Consequently, an increasing K D value with time was required in the DATES model to obtain successful D eff (θ) predictions. Since chemical-soil contact time and adsorption-desorption history typically vary in each compartment of a soil profile, transport models, including sorption kinetics, will become very complex and DATES with a time-dependent K D relation may represent a useful model alternative.

It has been assumed, but not proved, that the spatial weighting and sample volume of Time domain reflectometry (TDR) regarding bulk soil electrical conductivity (ECb) equal those determined for the relative dielectric permittivity (K). In this study, two types of experiments were carried out: (i) sensitivity experiments where the cumulative vertical weighting as a function of distance between the probe rods and the soil surface were determined for both K and ECb at two different soil water contents and (ii) solute diffusion experiments to evaluate the discrepancies between actual and TDR-measured relative ECb in the case where a steep gradient in ECb passes the probe. Three-rod TDR probes and a sandy loam soil were used in both experiments. The sensitivity experiments confirmed that TDR weights K and ECb equally in the transverse plane. Hence, previously established relationships to calculate the weighting function and sample area of a given TDR-probe geometry apply for both K and ECb. The diffusion experiments showed that if a steep vertical solute gradient passes a horizontally inserted TDR probe, the TDR-measured ECb profile will be more spread than the actual profile passing the probe. This phenomenon of artificial (TDR-induced) diffusion is caused by (i) TDR probes not representing a point measurement, and (ii) the nonlinear weighting of K and ECb in the transverse plane. As the steepness of the solute concentration profile diminishes the TDR-induced diffusion decreases rapidly and becomes negligible for most applications. The effect of TDR-probe geometry on the discrepancy between actual and TDR-measured relative concentration was examined theoretically for selected two- and three-rod probe configurations.

Accurate description of gas diffusivity (ratio of gas diffusion coefficients in soil and free air, D s /D 0 ) in undisturbed soils is a prerequisite for predicting in situ transport and fate of volatile organic chemicals and greenhouse gases. Reference point gas diffusivities (R p ) in completely dry soil were estimated for 20 undisturbed soils by assuming a power function relation between gas diffusivity and air-filled porosity (e). Among the classical gas diffusivity models, the Buckingham (1904) expression, equal to the soil total porosity squared, best described R p . Inasmuch as our previous works (Parts III, VII, VIII) implied a soil-type dependency of D s /D 0 (e) in undisturbed soils, the Buckingham R p expression was inserted in two soil- type-dependent D s /D 0 (e) models. One D s /D 0 (e) model is a function of pore-size distribution (the Campbell water retention parameter used in a modified Burdine capillary tube model), and the other is a calibrated, empirical function of soil texture (silt + sand fraction). Both the Buckingham-Burdine-Campbell (BBC) and the Buckingham/soil texture-based D s /D 0 (e) models described well the observed soil type effects on gas diffusivity and gave improved predictions compared with soil type independent models when tested against an independent data set for six undisturbed surface soils (11-46% clay). This study emphasizes that simple but soil-type-dependent power function D s /D 0 (e) models can adequately describe and predict gas diffusivity in undisturbed soil. We recommend the new BBC model as basis for modeling gas transport and reactions in undisturbed soil systems.

Salt diffusivity as a function of soil-water content and soil-water characteristic curves was measured on three sieved soils of different texture. The data were used together with ion diffusivity data for sieved soils from literature to test different diffusivity models. No significant differences between salt-, counter-, and self-diffusion data were observed, suggesting an insignificant effect of diffusion type in most cases. Two new models for predicting ion diffusivity, based on the Campbell soil-water retention model parameter b, were proposed: (i) a model with a b-dependent threshold water content θ(th) (soil-water content where the ion diffusivity approaches zero) and (ii) a power function model where the power term η, representing the liquid phase tortuosity, is a linear function of b. In both models, the diffusivity at the soil-water content equal to the total porosity was estimated from a simple impedance factor model. Both b-dependent models gave improved predictions of ion diffusivity compared with existing models. The b-dependent power function model with η = 0.3b gave better predictions than both the θ(th)-dependent model and a recent model for gas diffusivity in undisturbed soil (Part III of this series, Soil Sci. 161:366-375) where the tortuosity term η was best described as a function of b-1. For use of the new b-dependent ion diffusivity models in the absence of soil-water characteristic data, it is shown that b can be fairly accurately estimated from soil texture.