Homogenization of the high fat milk products. Application of the Markov chain for the description of a process

The method for development of the mathematical model of the process for milk products homogenization is given, The mathematical model is based on the Markov's chain with discrete states and continuous parameter for which homogenization pressure is accepted. To describe the processes of coalescence of fat globules during homogenization at large percentage of fat and homogenization pressures it is offered to use reverse transitions along with the direct ones. The model realization is carried out in the environment of MathWorks Simulink structural modeling. Identification of model's parameters was carried out by minimization the standard deviation calculated from the experimental data for each fraction of the fatty phase of milk products. As a set of experimental data results of processing of micrographs of distribution of the fat globules in the samples of whole milk which was exposed to homogenization with different pressures were used. As a method of optimization the Pattern Search method with search by algorithm of search of Latin Hypercube from Global Optimization Toolbox was used. The error of calculations based on the experimental data was on average about 3 % for all fractions (relative share of the fraction in the sample volume). The additional introduction of the reverse transition intensities allowed to reduce the error in the calculations by 23 %. The offered mathematical model allows to calculate a profile of volume or mass distribution of a fatty phase (fat globes) in a product depending on the pressure of homogenization. It can be used in the laboratory and scientific researches of milk products composition and for calculations, design and modeling of the technological equipment for the dairy industry enterprises.

milk products, homogenization, mathematical model of a process, the Markov chain