The mathematical model of the homogenization process of high-fat dairy products based on a Markov chain

The paper presents a method for synthesizing of mathematical model of the process of dairy products homogenization. The basis of the the mathematical model Markov's chain is with discrete and continuous states of the parameter for which the homogenisation pressure was taken. To describe the processes of adhesion of fat globules during homogenisation process for large percentage of fat and homogenization pressures it is proposed to use the reverse transitions along with the direct ones. Implementation of the model was performed in structural modeling environment MathWorks Simulink™. Identification of the model parameters was carried out by minimizing of the standard deviation of the calculated data from the experimental ones for each fraction of the fat phase of dairy products. As the set of experimental data the results of processing of microphotos of the fat globules distribution of whole milk samples were used. This milk was subjected to homogenization at different pressures. The method of optimization was Pattern Search method with the search algorithm Latin Hypercube from the Global Optimization Toolbox library. According to the experiment data the accuracy of calculations averaged over all fractions up to 3% (relative share of the fraction volume in the sample). The addition of the reverse transition intensities allowed to reduce the accuracy of calculations by 2-3%. The proposed mathematical model allows the calculation of the profile of the volume or mass distribution of the fat phase (fat globules) in the product, depending on the homogenization pressure and can be used in the laboratory and scientific researches of dairy products composition, as well as in the calculation, design and simulation of dairy industry technologycal equipment