On the size distribution of dispersed fractal particles

Using a thermodynamic approach, a disperse system formed by an ensemble of particles with various shapes and volumes is studied. The shape of a particle is set by the value of its fractal dimension, which characterizes the relationship between the volume and surface area. Using the methods of number theory and the Hardy–Ramanujan–Rademacher formula, the size distribution functions of the dispersed phase of particles with various shapes in the ensemble corresponding to the state of thermodynamic equilibrium are constructed. Based on the distribution functions, estimates of the mean size and fractal dimension of dispersed particles are obtained. The relationships between the average geometric characteristics of particles in the ensemble, the thermodynamic conditions in which the disperse system is located, and the properties of the substance forming it are established.