Hydrodynamics of two-layer media with piecewise constant densities and viscosities and particle sedimentation in the interplate space of a separator

Abstract

A model of the interplate flow of two immiscible homogeneous liquids with different constant densities and viscosities in a separator is considered. In the linear approximation (taking into account the smallness of the interplate gap), a set of equations is obtained for determining the velocities and pressure of the media and the liquid/liquid interface. The existence of a solution for the axisymmetric case is proved. The interface line between the media is plotted for various model parameters. A generalization of Bremer’s formula is obtained for the critical diameter of a sedimenting particle in the case of equal densities of the media.