Retaining structure of homogeneous fluid and granular stream is one of the main criteria for technological process assuring the high quality outcome in many industries, including mechanical engineering and oil & gas industry. For example, in oil and gas industry during the pipeline transportation of oils there is a strong trend for cluster aggregation, and particle coarsening and entanglement. Dehomogenization of particle stream results in reverse dynamics of the stream. The importance of prevention and minimization of small particles coalescence by separating the oil stream leads to the need of improving the properties of the dispersers to boost their efficiency. Our paper investigates the operating principle of the disperser for separating particles (separator), which is designed by the authors. We have considered a particle stream of dispersed structure. We have obtained the conformity with the stability of the disperser operation. To yield the results we use the extremum problems for differential equations. This approach provides strong evidence that there are optimum parameters of the dispersers, which result in better stability of the particle stream.