A knowledge of the mass fractal dimension of aggregated solids in edible oils, for example, can provide us with an understanding of the factors which affect diffusion in such systems and the system’s response to shear, such as identifying the boundaries of shear banding. Mass fractal values can also guide the manufacture of new products when looking to replace one of the ingredients. Some of the techniques which have been used to characterize fractal structures in edible fats and oils are (1) light microscopy and the box counting method, (2) neutron scattering and (3) X-ray scattering. The box counting method relies on the scaling of two-dimensional images of the solid structures as functions of the size of areas that become progressively smaller, while scattering methods rely on an interpretation of the scattering intensity, I(q), or the structure function, S(q), as a function of the scattering vector q. This talk will present a brief overview of the mathematics of these techniques and show how erroneous conclusions can arise from their use. Questions regarding, for example, (a) the discarding of information by dimensional reduction of the experimental data, (b) the ignoring of aspects of polydispersity in the experimental samples, and (c) the use of insufficient I(q) data, will be addressed. The perils associated with these approaches will be illustrated by computer simulation and animated graphics.
