Flow-regime analysis of non-Newtonian duct flows

Reoriented duct flows of generalised Newtonian fluids are an idealisation of non-Newtonian fluid flow inindustrial in-line mixers. Based on scaling analysis and computation we find that non-Newtonian duct flowshave several limit behaviours, in the sense that such flows can become (nearly) independent of one or moreof the rheological and dynamical control parameters, simplifying the general flow and mixing problem. Theselimit flows give several levels of modelling complexity to the full problem of non-Newtonian duct flow.We describe the sets of simplified flow models and their corresponding regions of validity. This flow-model decomposition captures the essential rheological and dynamical characteristics of the reoriented duct flows and enables a more efficient and systematic study and design of flow and mixing of non-Newtonian fluids in ducts. Key aspects of the flow-model decomposition are demonstrated via a specific, but representative, duct flow.