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.

High Stearic High Oleic Sunflower Oil Extraction: Influence of Temperature, Moisture, and Dehulling on Kinetic Parameters

“…Five terms of the series were needed to fit the kinetic model for the data obtained at 40 °C, and four terms for the other working temperature (because when more terms were added to the series, the adjustment parameters remained unchanged. [8,17] ). A five-term model was adopted to standardize the model to all temperatures.…”

“…), because when more terms were added to the series the adjusted kinetic parameters remained unchanged. [8,17] The obtained coefficients, as well as the results of the comparison of the non-linear models, are presented in Table 3.…”

“…moisture content) on oil extraction kinetics at 50 °C. For both samples, partially dehulled and undehulled, a seven-term model was adopted to fit the kinetic model for the data obtained (because when more terms were added to the series, the adjustment parameters were not modified [8,17] ).…”

“…[9][10][11]15] Franco et al [16] used the first three terms of the series to evaluate the diffusion coefficient during the oil extraction of rosehip seeds, reporting that the first term is generally used with little error for the extraction of plant matrices where external resistance is negligible. On the other hand, Sánchez et al [17] carried out a detailed analysis of the exponential series, pointing out that it is necessary to adopt an appropriate model simplification criterion for each particular system in order to avoid errors in the values of the model parameters and the interpretation of the phenomena involved.…”

“…On the other hand, Sánchez et al. [ 17 ] carried out a detailed analysis of the exponential series, pointing out that it is necessary to adopt an appropriate model simplification criterion for each particular system in order to avoid errors in the values of the model parameters and the interpretation of the phenomena involved.…”