The most commonly used empirical model for the quantity Q of a radioactive isotope leached from a solidified waste as a function of time t is Q = a(t to the 1/2 power) + bt, where a and b are empirically determined constants for a specific leach process involving a specific isotope. This formula works well for many solid wastes and can be derived theoretically from a model employing Fickian diffusion. However, the formula is known to be totally inaccurate for many other solids and also in particular for glassy solids which devitrify. Since devitrification and other symptoms of aging are commonly-occurring processes in the long term storage of radioactive waste, it is important to have a correct alternative formula for Q and even more important to understand the physical processes involved in leaching. A theoretical model involving a generalized, non-Fickian mechanism for diffusion is derived in this paper and applied to determine Q as a function of time t. It is found, on the basis of this type of diffusion which occurs in devitrified glassy solids and other solid waste materials, that Q=A(t to the 1/4 power) + B(t to the 3/4 power). Here A and B are constants which can be determined empirically, and they can also be determined phenomenologically in terms of the fundamental parameters of the diffusion model. When both formulas are normalized to a common value, at some instant the new formula predicts larger initial quantities and faster initial leach rates.

"January 1981"--Cover. Includes bibliographical references. "EPA 520/8-81-001."

Abstract -- Introduction -- Generalized diffusion model -- The time law for leaching -- Accounting for radioactive decay -- References -- Appendix A. Generalized diffusion equations -- Appendix B. Boundary conditions for the generalized diffused equation.