Transition of a partially yielded Casson fluid from circular to helical flow

In the Casson model, a fluid behaves as a solid for low stress but yields to flow as a viscoplastic fluid as the stress increases beyond a yield stress. The Casson model is often used to model the flow of blood or the flows occurring in food processing. We analyze the flow of a Casson fluid between infinitely long coaxial cylinders, with the inner cylinder rotating and the outer cylinder stationary, so that only the fluid adjacent to the inner cylinder yields. Simultaneously, axial flow arising from a small axial pressure gradient causes the flow to transform from a circular to a helical flow. Such flow is relevant to a number of applications, particularly rheometry. A perturbation analysis based on the pressure gradient provides explicit approximations for the fluid velocity proviles, as well as the change in location of the solid-fluid boundary. These approximations show the dependence of flow quantities on a range of fluid parameters, not just for specific parameter values, as occurs when numerical calculations are used.