Study of uncertainty in the fitting of diffusivity of Fick's Second Law of Diffusion with the use of Bootstrap Method

• Uncertainty in diffusivity estimation of Fick's Second Law of Diffusion.
• Bootstrap Method used to uncertainty inference on estimated parameters.
• Variability of diffusivity values low and stable with ten or more series terms.
• Erroneous interpretation may emerges if few terms of series solution are considered.

Through appropriate considerations, Fick's Second Law of Diffusion admits analytical solution. A model based on this law was proposed and its analytical solution in series was obtained for mathematically modeling the soybean hydration process. The diffusivities were fitted to experimental data by nonlinear regression. The Bootstrap method was used to assess uncertainties that occur in the estimation of diffusivity. The study was based on the analysis of the influence that the amount of terms of the series (analytical solution) exerts on the variability of the diffusivity values adjusted. The results showed that the variability of these values decreases considerably as more terms of the series are considered in analytical solution. From ten terms considered in the series, the variability of the diffusivity becomes stable. The results also showed that the number of terms of the series may compromise the correct interpretation of the influence of temperature in the diffusivity values.