Linear stability of Bingham fluids in spiral Couette flow

Abstract

The linear stability of Bingham-plastic fluid flow between two concentric cylinders rotating independently and with axial sliding of the inner cylinder (spiral Couette flow) is studied. Bingham fluid exhibits a yield stress in addition to the plastic viscosity, which has some inhibiting effects on the competition between the centrifugal and shear instability mechanisms owing to the inter-relationship of the azimuthal and axial velocities. Islands of instability, which are found in the spiral Couette flow of Newtonian fluids, may not exist owing to the effect of yield stress. The possibility of the yield surface falling between the cylinders is analysed. Although small perturbation waves appearing on the yield surface are considered, the yield surface, which has been treated as a free surface, has little effect on the flow stability. The effects of the axisymmetric and non-axisymmetric perturbation on flow stability are both presented. Both the rotation of the outer cylinder and a decrease of the gap between the cylinders have stabilizing effects.