VISCOPLASTIC FLOW IN CENTERED ANNULI, PIPES, AND SLOTS

A general method for the practical calculation of viscoplastic flows in centered annuli of arbitrary radius ratio is presented. The analysis is worked for the Casson, Herschel-Bulkley, and Robertson-Stiff rheological models, but the method is readily extended to other viscoplatic rheologies. A robust algorithm for the practical calculation of pressure drops and velocity profiles from given volumetric flow rates is presented, differing from other calculations where the pressure drop is the given parameter. Illustrative calculations are given for the Herschel-Bulkley model, together with a simple experimental test of pressure drop results for a particular case. Previously published results (also readily extended to other rheologies) for the simpler but related pipe and slot channel geometries are reviewed with some extensions for comparison with the annulus case.