Taylor-couette Instability of a Bingham Fluid

Stability of a Bingham fluid in Taylor-Couette flow is studied. Of interest is to determine the critical values of the inner and outer cylinder angular velocities which cause the linear instability in the system. We introduce a perturbation into the basic flow, and examine the linearized Navier-Stokes equations for the perturbation. Assuming a normal mode solution for the perturbation, we obtain an eigenvalue problem which determines when the perturbation will grow or decay with time. In the case of a plug region at the outer cylinder wall, additional boundary conditions are applied at the yield surface. The marginal stability curve is generated numerically using a finite difference method. In addition to numerical analysis, heuristic arguments and energy methods are applied to find a lower bound for stability.