Abstract <p>Mathematical modeling of the flow and separation processes of two-phase media in liquid plate separators with curved inserts has been considered. An algorithm for numerically calculating the variable values of the gap between the inserts and the angle of inclination of the walls relative to the rotation axis is proposed. The equations of motion for a two-phase medium in a quasi-homogeneous approximation are solved using the method of surfaces with equal flow rates. A calculation algorithm for the deposition of dispersed particles has been developed, taking into account the variability in the length of the deposition path and the direction of the centrifugal force relative to the curved channel walls. Numerical calculations were performed for parabolic and conical channels, considering the presence of an initial section with different medium and particle properties. A computational experiment was conducted to study different flow patterns and the separation process of a two-phase fluid.</p>