Mass balance soil diffusion

The conceptual model for diffusive soil transport down a hillslope is shown in Eigure 24 (Heimsath et al., 1997, 1999). In any given section of the landscape, the mass of soil present is the balance of transport in, transport out, and soil production (the conversion of rock or sediment to soil). If it is assumed that the processes have been operating for a sufficiently long period of time, then the soil thickness is at steady state. The model describing this condition is... 

Since this often applies to leaching experiments and to practical applications dealing with diffuse pollution, transport in soils is often treated as a one-dimensional problem. Using a 1-D mass balance equations, both concentration definitions are related through ... 

In this case the D values, which are conductivities, add reciprocally since the 1/D quantities are effectively resistances. The relative resistances become immediately apparent. In more complex situations, there may be several series and parallel resistances, an example being volatilization from soil in which there is diffusion in both soil air (pore air) and soil water (pore water) followed by an air boundary layer resistance. Later an example is given involving multiple transport processes and illustrates the simplicity and transparency of the fugacity mass balance equations. 

Our approach here is essentially that of McKone and Benett (2003), which is based on the Jury et al. (1983) model. It is incorporated within the latest version of the CalTOX model (McKone, 1993) and the original version of the TRIM (USEPA, 2003) model, but also used in other models such as BETR (MacLeod et al., 2001). This approach uses one or more soil compartment layers while maintaining a structure that links easily to other compartments such as air and vegetation in multimedia models. This approach begins by setting up the differential equations describing the mass balance in soil and accounting for diffusion in air and water phases, advection via water, bioturbation, and chemical transformation. Erom the steady-state analytical solution to these equations, which can be applied stepwise to different layers, one develops an equivalent compartment model that uses compartment-based inventories and transfer factors. 

In any defined horizontal layer of soil, the rate in mol d at which the dilute chemical mass inventory in that layer is changing is defined by balancing three processes. First there is dispersion due to both physical (diffusion) and biological (bioturbation) processes. Second is advection in soil fluids—primarily the downward (or upward)... 

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