Nonlinear stability of Poiseuille flow of a Bingham fluid: theoretical results and comparison with phenomenological criteria

We present new results on the nonlinear stability of Bingham fluid Poiseuil le flows in pipes and plane channels. These results show that the critical Reynolds number for transition, Rec, increases with Bingham number, B, at l east as fast as Re-c similar to B-1/2 as B --> infinity. Estimates for the rate of increase are also provided. We compare these bounds and existing li near stability bounds with predictions from a series of phenomenological cr iteria for transition, as B --> infinity, concluding that only Hanks [AIChE J. 9 (1963) 306; 15 (1) (1963) 25] criteria can possibly be compatible wit h the theoretical criteria as B --> infinity. In the more practical range o f application, 0 less than or equal to B less than or equal to 50, we show that there exists a large disparity between the different phenomenological criteria that have been proposed. (C) 2001 Elsevier Science B.V. All rights reserved.