Diffusion Coefficients in Soil

Most solutes in soils are to some extent adsorbed on the soil solid only a small fraction is in the solution in the pores. However some adsorbed solutes, particularly exchangeable cations, can have considerable mobility on soil surfaces (see below), so it is important to consider the solid phase pathway as well as the solution. Because the diffusing solute passes rapidly between the solid and solution, the two pathways partly act in series. In such a heterogeneous medium as soil it is not realistic to account for the mobilities and concentration gradients of solutes in all the constituent parts. But if the soil volumes and reaction times 

Following from this definition, the diffusive flux of a solute through the solution and solid in the x direction is given by (Tinker and Nye, 2000, Equation 4.17) 

The first term on the right-hand side of Equation (2.17) represents diffusion exclusively in solution the second term represents the additional diffusion that occurs as a result of mobility on the soil solid. 

The concentration of the solute in the solid is expressed in terms of the amount per unit weight of solid, Ss, by 0s Cs = pSs where p is the weight of dry solid per unit soil volume. By definition, F = —DdC/dx. Substituting for F and 0sCs in Equation (2.17) and rearranging gives 

In the following sections I discuss the components of the diffusion coefficient so defined in turn. Note all the components of D are altered by flooding the soil. As well as increasing the cross-sectional area for diffusion, represented by flooding affects the geometry and tortuosity of the soil pore network, represented by /l and fs, and solute sorption on the soil solid, represented by dCt/dC. 

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The ratio of the effective diffusion coefficient in soils or mineral materials to the diffusion coefficient in free water is, however, also influenced by other effects than only the complexity of the diffusion paths in the pore spaces of a soil. For example, the viscosity of water can decrease in narrow pore spaces, with corresponding effects on the diffusion coefficients of the dissolved substances. Apparent tortuosity factors calculated from measured values can therefore be smaller than the value suggested by geometry. It is therefore justifiable to find a conservative estimate of diffusion coefficients for pollutants in soil water, for example when considering mineral landfill liners for which no measured values are available, to use this pure... 

Table 7.6. Diffusion coefficients of organic substances at 20 °C in dilute aqueous solution and effective diffusion coefficient in soil water of mineral liners calculated with r= 1/3 and diffusion coefficient in the HOPE geomembrane at a small concentration. The units for the diffusion coefficient should be considered (Muller etal. 1997a)...

Table I shows the results of calculating a soil diffusion coefficient and soil diffusion half-lives for the pesticides. The 10% moisture level specified means that the soil is relatively dry and that 40% of the soil volume is air available for diffusion. Complete calculations were not made for methoxychlor, lindane, and malathion because, based on Goring s criteria for the Henry s law constant, they are not volatile enough to diffuse significantly in the gas phase. This lack of volatility is reflected in their low values of X. These materials would move upward in the soil only if carried "by water that was moving upward to replace the water lost through evapotranspiration at the surface. Mirex has a very high Henry s law constant. On the basis of Goring s criteria, Mirex should diffuse in the soil air but, because of its strong adsorption, it has a very large a and consequently a very small soil air diffusion coefficient. The behavior of Mirex shows that Goring s criteria must be applied carefully.

Olesen T, Moldrup P, Yamaguchi T, Rolston DE. 2001. Constant slope impedance factor model for predicting the solute diffusion coefficient in unsaturated soil. Soil Science 166 89-96. 

Staunton S. 1990. A comparison of the surface impedance factors of Ca, Na, Rb and Cs derived from their self-diffusion coefficients in various soils. Journal of Soil Science 41 643-653. 

Solution of equations 5-1 and 5-2 requires site-specific values as well as chemical-specific values. Critical chemical-specific properties in the above equations are the Henry s law constant (H), the organic carbon/water partition coefficient (Koc), and the effective diffusion coefficient through soil (Deff). Henry s law constants are estimated using solubility and vapor pressure values obtained from data compilations. The Koc is estimated from the octanol-water coefficient (Kow) and is commonly estimated from the Hansch and Leo (1979) fragment constant approach (TPHCWG 1997b) ... 

Where is the whole sediment or soil diffusion coefficient in terms of area of sediment or soil per unit time, and Dq is free ion diffusion coefficient measure in bulk solution (Berner, 1980). 

Light transmission L. L. Schramm and J.C.T. Kwak, op. cit. Electrophoretic mobility P. Bar-On, I. Shainberg, and I. Michaeli, Electrophoretic mobility of montmorillonite particles saturated with Na/Ca ions, J. Colloid Interface Sci. 33 471 (1970). Intrinsic viscosity I. Shainberg and H. Otoh, op. cit. Chloride exclusion volume J. E. Dufey, A. Banin, H. G. Laudelout, juid Y. Chen, Particle shape and sodium self-diffusion coefficient in mixed sodium-calcium montmorillonite. Soil Sci. Soc. Am. J. 40 310 (1976). 

Numerous measurements of effective diffusion coefficients in mineral liner materials, as they are typically used for landfill liners, are available for cations and anions. In an extensive investigation, H. L Jessberger and collaborators looked into the diffusion coefficients of various test liquids (mono solutions and mixtures of the chlorides, nitrates and sulphates of the metals listed in Table 7.7, organic mono solutions and mixtures and an artificial leachate) in different mineral liner materials (natural clayey soils and different kinds of well-graded mineral mixtures with various additives) (Jessberger et al. 1995). A systematic relationship between characteristic... 

Diffusion coefficient for soil 1x10 mVs N/a This value is from GiRiA Report 152 for a soil with a voids ratio of 0.25. The soils in this site are unlikely to have a voids ratio greater than 0.3 and the table in GiRiA 152 indicates this will not significantly affect the diffusion coefficient... 

Figure 2 Gradients in Rb around a maize root as visualized by autoradiography. The depletion of Rb depends on the diffusion coefficient (D,.) which in turn depends on the soil texture. (From Ref. 12.)...

The effective diffusion coefficient of a solute in soil is thus... 

The level of vapor movement in the unsaturated zone is much less important than transport in liquid form. However, this might not be true if the water content of the soil is very low or if there is a strong temperature gradient. The movement of vapor through the unsaturated zone is a function of temperature, humidity gradients, and molecular diffusion coefficients for water vapor in the soil. 

The order of the mobilities of alachlor, butylate, and metolachlor in columns of various soils was metolachlor > alachlor > butylate. This correlates directly with the water solubilities and inversely to the adsorption coefficients and octanol/water partition coefficients of these compounds. Diffusion of these compounds in soil thin-layers was as follows butylate > alachlor > metolachlor, which correlates directly with the vapor pressures of these compounds. Significant soil properties affecting diffusion appeared to be bulk density and temperature. Soil moisture is also probably important, but its effect on the diffusion of these compounds was not determined. 

Transport of the herbicides by vapor diffusion on moist soil was shown to be directly related to vapor pressure and inversely related to water solubility. Transport of the herbicides by leaching was shown to be inversely related to the Freundlich adsorption coefficient which in turn was directly related to the octanol/water partition coefficient and inversely related to water solubility (16). 

An intact polythene membrane within the concrete base of a building will prevent pressure driven flow of radon into the building from the soil, even if the concrete is cracked. Diffusive flow of radon into the building will also be reduced because of the comparatively low diffusion coefficient of radon in polythene ( v 10 7 cm2 s"1). No significant improvement was achieved by substituting a 50 ym sheet of mylar for polythene (mylar diffusion coefficient x 10"11 cm2 s"1). In this case additional difficulties were experienced in sealing the less flexible material to the walls. 

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