Maximum entropy method in comminution modelling

摘要

This paper analyses the comminution process. There are two random functions: the selection function and the breakage function in the stochastic model based on population balance. Introducing the energy balance, applying the maximum informational entropy method and taking into consideration the normalized condition, enables us to formulate and solve the variational problem and determine the breakage function by Lagrange's multipliers method. The above determination of the breakage function is an original new method. The sought form of the breakage function is an argument of the constrained extremum of an integral functional with two indirect conditions. The obtained form of the breakage function was applied to the equation of the population balance. This leads to the prediction of the particle size distribution of the single comminution product with an additional assumption concerning the form of the selection function.