Experimental and Mathematical Description of Nonadsorbed Solute Transfer by Diffusion in Spherical Aggregates

Abstract Diffusion of nonadsorbed solutes ( 3 H 2 O and 36 Cl ‐ ) out of two sizes of porous ceramic spheres (0.55‐ and 0.75‐cm radius) was measured. These data were analyzed to provide independent estimates of the input parameters required in two simulation models for describing solute transport in aggregated porous media with distinct mobile and stagnant pore‐water regions. Tracer‐saturated porous spheres were placed in tracer‐free 0.01 N CaCl 2 solution and the rate of tracer diffusion out of the porous spheres was measured by monitoring the increase in tracer concentration with time in the external electrolyte solution. Experimental results were analyzed using two mathematical models. Fick's second law, written in spherical coordinates, formed the basis for Model I. In Model II, the time‐rate of solute transfer into or out of the porous spheres was assumed to be proportional to the difference in tracer concentration inside and outside the porous spheres. The analytical solution to Model I for given initial and boundary conditions was substituted into Model II, to derive an explicit expression relating the empirical mass transfer rate coefficient (α) in Model II and known physical constants of the system. This theoretical analysis indicated that the α value is dependent upon the sphere radius, time of diffusion, volumetric water contents inside and outside the sphere, and the molecular diffusion coefficient. Over a range of experimental conditions, excellent agreement was found between measured α values and those calculated using the analytic expression developed here.

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