Theory for flow of Casson and Herschel-Bulkley fluids in cone-plate viscometers

Abstract

Mathematical models for blood flow in cone-plate viscometer have been considered, by assuming blood as a Casson/Herschel-Bulkley fluid. Three different cases have been analyzed (i) when there is no shearing, (ii) partial shearing and (iii) full shearing. The relationships between the angular velocity and torque have been obtained for the above three cases. By assuming total shearing, the analytical expression for apparent viscosity has been obtained. Variation of apparent viscosity with yield stress, angular velocity, Casson co-efficient of viscosity, consistency index and flow behaviour index has been computed. It is observed that as the angular velocity increases, the apparent viscosity decreases for both fluids. Further, it is found that as the cone angle increases, the apparent viscosity increases. This behaviour of apparent viscosity in cone-plate viscometer is interesting and unexpected and is being reported first time.