Computer simulation of fractal dimensions of fat crystal networks

The rheological properties of fat‐structured products are determined by the microstructure of their fat crystal networks, which can be quantified by using microscopical and rheological techniques. Of particular interest to this study is the quantification of the fractal dimension of the network using these two techniques. Fractal dimensions determined by polarized light microscopy include box‐counting, particle‐counting, and Fouriertransform fractal dimensions, whereas the fractal dimensions determined by small deformation dynamic rheology exploit the dependence of the storage modulus on the solids' volume fraction. This work reveals that different microscopy fractal dimensions are sensitive to different microstructural factors within the fat crystal network, and thus have different physical meanings. The boxcounting fractal dimension, Db, increases with increases in crystal size and area fraction of the fat crystals, whereas the particlecounting fractal dimension, Df, is sensitive to the radial distribution pattern of fat crystals; and the Fourier‐transform fractal dimension, DFT, decreases with increasing crystal size. In the studies on the macroscopic physical properties of fat crystal networks, it is necessary to find the determining structural characteristics and then use the fractal dimensions that are most closely related.