Fractal pore-size distribution on freeze-dried agar-texturized fruit surfaces

Freeze-dried texturized fruits were produced by freeze-dehydrating gels consisting of fruit concentrate or puree. The products were dry and crunchy with a high content of fruit ingredients. A dried texturized fruit product is characterized by its porosity and pore-size distribution, among other parameters. The objective of this work was to examine the possibility of assessing edible products by modifying a technique, which was first suggested by the Czech scientist Korcak, ∼65 years ago, for studies in the fields of geography and cartography. We were interested in whether this procedure would be suitable for describing the distribution of pore sizes within a dried texturized fruit section or any other solid. We hypothesized that instead of dealing with ‘pieces’ of land (islands or archipelagos, as suggested originally) suspended in water (seas and oceans), as is the case in cartography, it is possible to reverse the picture, and imagine the solid fragments as ‘holes’ or ‘pores’ within a solid matrix, and thus develop a new estimate of porosity. Another objective of this research was to test whether the calculated fractal index would be sensitive to food-processing conditions. We observed that for randomly selected, large enough pores within the freeze-dried texturized fruit, the average fractal dimension of the circumscribing silhouette of the pores is about twice the measure of the size distribution of a set of pores as estimated by Mandelbroth. The fractal dimension of the pore ‘coastline’ is a property of the individual pores, whereas the fractal index deduced from the Korcak plot is a property of the group of pores. This size-distribution measure was also related to the porosity of the texturized fruit. The proposed approach can be generally used to identify changes in the porosity of cellular solids, independent of their origin (i.e. edible or not), and as a simple tool for product development.