YIELD SURFACES FOR HERSCHEL-BULKLEY FLOWS IN COMPLEX GEOMETRIES

Rectilinear flows of Herschel-Bulkley materials in complicated geometr ies are considered. The flows are considered in the limit when a param eter related to the yield stress is small. In this limit, asymptotic m ethods are used to determine the shape of the yield surfaces. The Hers chel-Bulkley flows are asymptotically matched with solutions found in the same geometries, and with the same boundary conditions, but for th e 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 scop e of application of such solutions, and it increases their utility. Se veral cases are considered in detail to illustrate the variety of situ ations which can occur. An exact solution is found for a problem in a simpler geometry, and the accuracy of the asymptotic method is demonst rated.