Modelling the transport of lactic acid, sodium chloride and reducing sugars in carrot slices submerged in brines - Part II. Multivariate approach

In this paper, following a methodology of (nested) increasing model complexity, it was found that the apparent diffusivities and the partition coefficients associated with the transport of lactic acid and sodium chloride from the brine into carrot slices submerged therein can be modelled as functions of temperature using Arrhenius-type relationships and as exponential functions of the initial concentrations of either solute in the brine. The apparent diffusivities in the free liquid phase, in the case of transport of reducing sugars from the carrots to the brine, are assumed to vary with time as a consequence of the bursting of the carrot cells following first-order kinetics on both the concentration of intact cells and dead cells. In this case, and following a similar methodology, the apparent diffusivity in the free liquid phase, the pseudo-first-order rate constant for cell bursting, and the partition coefficients are well modelled when they are all assumed to follow temperature dependencies given by Arrhenius-type relationships; the dependencies on the initial concentration of salt in the brine were found not to be statistically significant. The underlying assumptions of normal distribution and constant variance were checked using plots of residuals, whereas the decision on the acceptable complexity of the nested models was taken based on the values of the F-distribution. The analysis developed is relevant for practical purposes because the multivariate models obtained in the form of correlations are simple functions of easily measured operating variables.