Mathematical modelling of the milk products homogenization process with application of Markov's chain

An approach to the development of a mathematical model of the process of homogenization of milk or milk products based on Markov’s chains is presented that allows estimate the mass (volume) distribution of the fat phase in the product. The developed mathematical model allows calculate the mass (volume) distribution of the fat globules depending on the pressure. The presented mathematical model can also be used for more profound research of milk or milk products homogenization process at construction of new types of homogenizing equipment, as it allows evaluate the behavior of each fraction of mass or volume distribution of the fat globules in the process of homogenization. To describe the structure of the mathematical model the Markov’s chain was chosen with discrete states and continuous parameter (pressure of homogenization process). The mathematical model has been implemented in an environment of structural modelling MathWorks Simulink™. Estimation of the model parameters was performed using a set of experimental data received in the course of processing of photomicrographs of the whole milk samples that were homogenized at different pressures. Parameters estimation was carried out by minimizing the average deviation calculated from the experimental data for each fraction. The Pattern Search method with Latin Hypercube procedure from the Global Optimization Toolbox library was used. The average relative error of calculations for all factions was 0,88 %, the maximum relative error was 3,7 % at the pressure of homogenization 30 MPa, which is apparently due to rather sharp changes in the properties of milk at the beginning of homogenizing process and absence of experimental data of homogenization process at pressures below 30 MPa.

homogenization, milk products, parameters of the process