Dean instability of bingham fluids in tangential flow between two fixed concentric cylinders

Abstract

In the present work, hydrodynamic instability of viscoplastic fluids is investigated in azimuthal pressure-driven flow between two fixed concentric cylinders-the so-called Dean flow. To avoid stress discontinuity anywhere in the gap, a regularized Bingham model was used to represent viscoplastic fluids. To determine conditions for the onset of instability, an infinitesimal disturbance was introduced to the basic flow and its evolution in time was checked using a normal-mode linear stability analysis. An eigenvalue problem was obtained which was solved numerically using the pseudo-spectral collocation method. A plot of the Dean number versus the Bingham number showed that the yield stress has always a stabilizing effect on the Dean flow. That is to say that, the critical Dean number is increased the higher the Bingham number. Results obtained at three different gap spacing suggest that by an increase in the gap size the flow becomes progressively more stable, but, only if the Bingham number is sufficiently low. At high enough Bingham numbers, however, it is predicted that by an increase in the gap size, Dean flow may become less stable. © 2010 The Society of Rheology, Japan.