Boltzmann Equation In The Modeling Of Mineral Processing

Abstract

Abstract The paper presents an application of the Boltzmann kinetic equation to the simultaneous modeling of multi-dimensional processes. This equation defines the evolution of the distribution of the probability density in a given phase space. In the case of a grinding process, the considered phase space is defined by the Cartesian coordinates of particle position, the components of particle velocity and the particle size. The theory of Markov processes is used in the paper to solve the Boltzmann equation for the multi-dimensional space of system states. In order to verify the presented model, research into the simultaneous comminution and movement of material in a drum ball mill was performed. The methodology developed to solve the Boltzmann equation significantly reduces the computational time, which is particularly important in the solution of multi-dimensional problems.