Computation of the flow of a two-layer fluid near a rotating wall under spin-up

This theoretical study considers a disk having a circularcavity of rectangular cross section filled with two immiscible viscous fluids and rotating about the z-axis. During an extended uniform rotation the interface between the fluids becomes vertical and all components of the velocity vector in a cylindrical coordinate system attached to the spinning disk are zero. As the angular velocity of the disk increases the particles of sluid immediately adjacent to the horizontal walls of the cavity acquire an additional angular velocity and initiate a radial flow under the action of the increased centrifugal force. This class of flows has been studied fairly completely for a homogenous fluid. At the same time no theoretical study has yet been made of the dynamics of a two-layer fluid. On the basis of these investigations one can conclude that the proposed mathematical and numerical models of the flow of a two-layer fluid in a boundary layer is an adequate description of the process and can be used to study the optimization of modes of functioning of a centrifuge.