This article is a continuation of the research, centering on a vacuum-filtration system, which is designed to reduce the concentration of calcium in water; a process is also known as—water softening. The problem of solving the concentration distribution of the initial (embryonic) particles of CaCO₃-particles, which were introduced into the limited volume of the apparatus with a turbine agitator-pump, is addressed through the use of diffusion and deterministic-stochastic models of mass transfer. The solution of the extreme problem allows determining the most important process parameters, such as time of dispersions homogenization and the dispersion mass flow rate to the surface of a special filter. For these parameters a comparative analysis of the adequacy of the theory was found through experiments, performed in the study. We found that uniform distribution of concentrations along the height of the apparatus is achieved by the angular velocity of the rotation 400 rpm for the turbine with 6 - 7 blades at the time of homogenization 14s. In this case, the dispersion mass flow to the surface of the cylindrical filter is 3 50 mg/s at an average concentration of the introduced CaCO₃ particles, which is equal to 10 g/L. We determined that the accuracy of the results depends on: the coordinates of the material input in the apparatus volume, the surface shape of the filter and the volumetric flow rate of the liquid (water), being discarded by the turbine blades in the normal direction to their surface.