Homogeneous diffusion layer model of dissolution incorporating the initial transient phase

On the estimate of the rate constant in the homogeneous dissolution model

The aim is to determine how well the rate parameter of the homogeneous model of dissolution can be estimated in dependency on the chosen times to measure the empirical data. The approach is based on the theory of Fisher information. We show that if the probability distribution of the measurement errors is known, the data should be collected at a single time instant or its close proximity in order to obtain the best estimate. This is in sharp contrast with commonly used experimental protocols. Further, from the properties of the Fisher information we deduce how suitable is the model of measurement error and we show that asymmetric distribution of data close to the time origin is unavoidable.