An approach to the application of a modified Fick’s diffusion model: Development of an algorithm

Abstract

In the present work, we studied the mathematical characteristics of a modified Fick’s diffusion model which is widely used for modelling the extraction kinetics of various compounds because it allows to describe the mass transfer in terms of two parameters: washing fraction (M0/M∞) and diffusion coefficients (Deff). This model also involves an infinite series of terms, obtaining an adequate simplification criterion of the model for each system under study. A calculation algorithm was developed to determine the number of terms of the series that is sufficient. Based on the developed criterion, the data obtained by various authors for different systems were analyzed, finding in general that the number of terms of the series was underestimated, which affected both the parameter values and the analysis of the phenomena involved. The main impact was detected on the parameter associated with the washing phenomenon, observing in general an underestimation of that parameter, whereas a smaller overestimation could be seen for the diffusion coefficient. Our study shows the importance of adopting an adequate simplification criterion when using a diffusion model to avoid errors in the interpretation of the mass transfer phenomena involved.