The issues of modeling the formation of a two-phase liquid-solid particle system in devices operating on the principle of mixing and dispersion. For this purpose, static formulas have been compiled for such parameters as the rate of discharge of clay extraction and the power consumption for washing sand, the speed of rotation of the liquid with untreated sand, the influence of the ratio of geometric dimensions on the above parameters has been considered. A static model has been compiled that allows us to identify patterns of changes in these parameters. Based on the obtained waveforms from the simulation of the model, conclusions were made according to which, when constructing an automatic control system for sand washing, it is necessary to ensure stabilization by such basic indicators as the required sand-clay ratio, the humidity of the cleaned sand, power consumption.