Added release time in diffusion/dissolution coupled release

While increasingly sophisticated models have been developed to more accurately predict dispersed solute release from complex systems, distillation of their results into quantitative trends has been difficult. Here, the numerically calculated release profiles of coupled diffusion/dissolution systems are quantified by their cumulative release time (CRT) and compared against corresponding diffusion-controlled limits. The increase in CRT due to a finite dissolution rate was found to vary inversely with the second Damköhler number across several orders of magnitude, and also vary linearly with the amount of solid drug loaded in the system. The analytical nature of the relationship provides new physical insights into the system and appears to be indifferent to the form of the secondary rate-limiting step. This work provides a simple analytical expression with which one can not only predict the mean release time for a given set of parameter values, but understand precisely how each parameter value will affect it. The simplicity of the correlation and the lack of apparent limits to its validity also suggest the existence of an analytical pathway for its derivation, which may yield additional insights into the effect of secondary rate processes on controlled release.

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