Yield surfaces for Herschel-Bulkley flows in complex geometries

Rectilinear flows of Herschel-Bulkley materials in complicated geometries are considered. The flows are considered in the limit when a parameter related to the yield stress is small. In this limit, asymptotic methods are used to determine the shape of the yield surfaces. The Herschel-Bulkley flows are asymptotically matched with solutions found in the same geometries, and with the same boundary conditions, but for the power-law model. A considerable number of exact solutions exist for the power-law material in a wide variety of different geometries with different boundary conditions. The asymptotic method broadens the scope of application of such solutions, and it increases their utility. Several cases are considered in detail to illustrate the variety of situations which can occur. An exact solution is found for a problem in a simpler geometry, and the accuracy of the asymptotic method is demonstrated.