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.

Analytic Solutions: Steady Flows

“…The boundary conditions on w(r) can be changed to include axial sliding of one or both cylinders; see Peng and Zhu [3] for the case when w(R 1 ) = U, w(R 2 ) = 0, and there is no pressure gradient along the axis of the pipe. In the helical flow, there are two non-zero shear stresses, viz., S rθ and S rz , and the equations of motion can be obtained from a combination of (5.…”

“…As an example of a flow problem without any approximation, consider the motion of a Bingham fluid caused by the rotation of the cylindrical surfaces and the axial movement of the inner cylinder, in the absence of a pressure gradient [3]. In such a flow, the fluid outside the yield surface will be in a state of rigid body rotation only.…”

Dean Instability of Bingham Fluids in Tangential Flow between Two Fixed Concentric Cylinders

“…As to the Dean instability of non-Newtonian fluids, most studies carried out in the past are in relation to viscoelastic fluids [16][17][18][19][20][21][22][23][24][25] or purely-viscous fluids. [26][27][28][29][30][31][32][33][34][35] In contrast, Dean instability of viscoplastic fluids has not been investigated to the same extent. This is quite surprising realizing the fact that viscoplastic (or yield-stress) fluids are quite common in industry.…”

“…37,38) Instability of Bingham fluids has been addressed in Taylor-Couette flow [26][27][28][29] , in plane Poiseuille flow [30][31][32][33] , and in annular pressure-driven flow. 34) Similarly, Dean instability of Bingham fluids has been investigated in curved pipes by Das 35) , and in curved rectangular ducts by Fellouah.…”

Stability of flow between rotating cylinders with axial buoyancy effect

“…Examples include the competitions between buoyancy and shear in inclined natural convection [1] , between rotation and buoyancy in binary mixtures [2] , between rotation and shear in Hagen-Poiseuille flow [3] , between rotation and axial sliding in Taylor-Couette flow [4] , and between rotation and axial pressure gradient in spiral Poiseuille flow [5] . Peng & Zhu [6] studied the problem in their most recent work on Bingham-plastic fluid flow in spiral Couette flow with axial sliding and found inhibiting effects on the competition. www.scichina.com www.springerlink.com…”