Approximate fractal morphometry of spherical type essential oil microemulsions: A simple model

In the present study, the approximate fractal morphometry of spherical-type essential oil microemulsions was performed. The geometric fractal characterization was carried out by a recently published continuous half-fractal model which allowed to model microemulsions as systems in their stable thermodynamic equilibrium phase with high degree of homogeneity. Regarding the characteristic of high homogeneity an equation was obtained to roughly describe the volume fractal dimension and the fractal volume of two special cases elaborated from Rosmarinus officinalis and Melaleuca alternifolia previously investigated. In addition, referring to the characteristic of high homogeneity, it was possible to approximate the fractal dimension of area and the fractal area for each microemulsion. Our numerical estimates showed coherence with the principles of Hausdorff-Besicovitch geometry and with the experimental evidence about the physical dimension as a non-integer dimension.