Abstract
A new model for the diffusion of oxygen in spherical aggregates of soils with simultaneous consumption at constant, linear, and nonlinear rate is proposed. To evaluate the effects of the dynamics of soil domain in which the diffusion and consumption takes place, a free-boundary formulation is studied. The three resultant free-boundary models are solved by a modification of the Constrained Integral Method. The obtained results are consistent with those presented by earlier authors who have solved the problems using fixed domains. The results obtained by our model for diffusion with constant consumption slightly overpredict the experimental values with respect to the results obtained by Currie (J Currie. Gaseous diffusion in the aeration of aggregated soil. Soil Sci. 1961;92:40-45) in fixed domains. Moreover, the results obtained by our model for diffusion with simultaneous nonlinear consumption overpredict the experimental values, partially improving the underpredicted results of Sierra et al. (J Sierra, P Renault, and V Valles. Anaerobiosis in saturated soil aggregates: modelling and experiment. Eur J Soil Sci. 1995;46:519-531) in fixed domains. Thus, our model could represent an alternative method to study and to generalize existing models.
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