Stability of circular Couette flow of binary mixtures

Abstract

The hydrodynamic stability of an ideal mixture of two viscous, dissimilar liquids contained between two concentric rotating cylinders is analyzed. The basic flow of the mixture is determined by coupling the mass and momentum equations with an equation for the equilibrium concentration distribution. Infinitesimal, axisymmetric disturbances are assumed, and the disturbance equations are written for the limiting case of large Schmidt numbers (no diffusion).The presence of density and viscosity variations leads to a twelfth-order eigenvalue problem with two-point boundary conditions that has the appearance of a combined Taylor and density-stratified shear flow problem. A numerical technique is devised to determine the stability boundary and to calculate Taylor numbers and oscillation frequencies for different growth rates.It is found that very small mean density gradients alter the critical Taylor number and that oscillations occurring in both the growing and neutral solutions are the dominant mode.