On the stability of viscous flow between two rotating nonconcentric cylinders

Abstract

The stability of viscous flow between two rotating nonconcentric cylinders is investigated with respect to infinitesimal disturbances. After the finite gap disturbance equations are formulated, the small gap disturbance equations are obtained. An approximate solution to the resulting eigenvalue problem is obtained by employing a perturbation method. A formula for calculating the critical Taylor number is deduced which is valid for small gap, small eccentricity and for the case when the outer cylinder is fixed. The mathematical model formulated gives rise to a local stability analysis. For θ = 0 o the eccentricity destabilizes the flow for small values of eccentricity ratio—the flow is less stable than when the cylinders are concentric. The results of a number of experimental and theoretical investigations are discussed.