Abstract

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.

中文翻译：

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关于分散形分形粒子的尺寸分布

摘要

使用热力学方法，研究了由各种形状和体积的粒子集合形成的分散系统。粒子的形状由其分形维数的值设置，该维数表征了体积与表面积之间的关系。使用数论方法和Hardy–Ramanujan–Rademacher公式，构建了与热力学平衡状态相对应的整体中具有各种形状的粒子分散相的尺寸分布函数。基于分布函数，可以获得对分散颗粒的平均尺寸和分形维数的估计。集合体中粒子的平均几何特征与分散系统所处的热力学条件之间的关系，