An empirical model linking solution volume-to-surface area ratio to the dissolution kinetics of oxides in aqueous systems

Understanding how environmental variables influence the dissolution rate of nuclear waste materials in aqueous systems is crucial for developing durable nuclear waste forms. In experiments to estimate dissolution rates, the amount of aqueous solution reacting with the material surface is often used as a convenient variable to control the solution saturation state, which then controls the dissolution rate. An exponential function between the dissolution rate and the solution volume-to-surface area ratio was derived, based on an empirical relation of a power function between the Gibbs free energy of dissolution and the volume-to-surface ratio. The relationship was employed to model the dissolution rates of several oxide minerals. The results suggest that the relationship is robust in numerically describing the dissolution rates as a function of the volume-to-surface ratio. Applying the relationship to the dissolution datasets of a nuclear glass and a ceramic nuclear waste form demonstrates its applicability to nuclear materials, providing important insights into the saturation state of the experimental conditions and the chemical durability of these materials. The proposed empirical relationship provides a convenient tool to help design dissolution experiments and offers important insights into the dissolution behavior of materials.