Among the numerous models developed to predict the shrinkage of materials during drying, the model developed by Katekawa and Silva [1] gives a general relationship between shrinkage and porosity with a limited number of parameters such as initial density of the wet product, true density of the solid phase, and true density of the liquid phase. A graphical interpretation of this model is proposed to visualize the changes of porosity by comparing the experimental shrinkage curve with an ideal one. Four examples are given to illustrate the applicability of the model using different materials (carrot, banana, xerogel, and sludge), two types of the solvent (water, isopropanol), and two drying technologies (convective drying, freeze drying). Porosity calculations were found to be very consistent and complementary with porosity measurements.

Based on a very simple model of mass conservation, three experimental properties (solid density, liquid density and initial bulk density) and the simultaneous acquisition of the reduced moisture content and the volume shrinkage during drying, a simple method is proposed to calculate the bulk porosity of a material during drying. This model allows a graphical interpretation to visualize the porosity change by comparing the experimental shrinkage curve with an ideal shrinkage curve. In the present work, several examples were taken from the literature to illustrate the application of this method to foodstuffs (apple, banana, carrot, garlic, pear, potato and sweet potato) with two different processes (convective drying, freeze-drying) and different drying conditions. Porosity calculations including error estimations showed a good agreement with experimental values reported in the literature.

A novel non-intrusive technique (stereo-correlation) was used to determine the apparent volume of a banana in convective drying condition. The volume was calculated using the 3D Digital Image Correlation method (3D-DIC), which provides the 3D shape of the banana during drying. The combination of this technique and mass measurement allows the calculation of the porosity using the model of Katekawa and Silva [1] and the graphical interpretation presented by Madiouli et al. [2] The banana shows an ideal shrinkage at the beginning of drying but stops shrinking at low moisture content, thus increasing the porosity up to 30-35%. The comparison of the experimental shrinkage and the calculated porosity with the experiments deduced from the literature enables us to conclude the effectiveness of the 3D-DIC technique as well as the porosity calculation model.

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