The equation of the modulator's passing cross-section area in the pulsation device with the vibrating rotor

Abstract

The article provides an analysis of the existing analytical models of the change in the cross-sectional area of the modulator in rotary-pulsation devices. The peculiarities of the application of such functions for the pulsation devices with the vibrating rotor are determined, taking into account the predominant mechanism of dispersion of emulsions. Using classical hydraulic and mathematical dependencies, in order to fulfill the requirement of creating harmonic pulsations of the emulsion in the modulator holes for synchronization with the axial oscillations of the rotor and the equality of the conditions of pulsations of the speed of the emulsion in each channel of the stator and rotor, the equation of the change in the cross-sectional area of the modulator in the pulsation devices with the vibrating rotor is determined in the form of a continuous function. This greatly simplifies the mathematical description of the function, and the subsequent analytical model of the movement of the emulsion in devices of this type. The resulting equation is necessary in determining such characteristics as the instantaneous speed and acceleration of the emulsion and the diameter of the dispersed phase after treatment.