Design of experiments for improving the precision in the estimation of diffusion parameters under isothermal and non-isothermal conditions

Mass transfer in food processing can often be described by Fick's second law, with diffusivity increasing with temperature according to an Arrhenius-type relationship. For predictive purposes it is most important to determine with high precision and accuracy these model parameters: the diffusivity at a given temperature, the activation energy and the pre-exponential factor for a range of temperatures. The main objective of this work was to define optimal experimental conditions for a process controlled by internal diffusion, on the basis of the concept of D-optimal design, both for isothermal and non-isothermal conditions. It was concluded that, for a spherical geometry and at a given temperature, experiments should consist of a number of replicates taken at the time required to reach a fractional loss/uptake of solute of 0.716. Two experiments should be conducted, one at each of the extreme temperatures of the range tested. Under non-isothermal conditions the optimal design is more complex, as it also depends on the heating rate. It was further concluded that, although the definition of the experimental design requires preliminary estimates of the parameters, deviations between the 'guessed' and the 'true' values do not seriously compromise the results.