Pushing the limits of generalized Newtonian fluid constitutive equations

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Highly complex non-Newtonian fluid behaviour plays a role in numerous industrial settings. Accurately capturing this behaviour can be extremely challenging. This PhD project explores the ways in which a relatively simple 'generalised Newtonian' framework can be used to capture complex rheological behaviour, including so-called 'normal stress differences', that is more commonly associated with elaborate visco-elastic, frame-invariant constructions. In particular, the project will explore and analyse the way in which an anisotropic viscosity tensor can be used to capture some of this behaviour. The project will first explore the ways in which a tensorial viscosity can be formulated to capture anisotropic effects in a suitably invariant fashion in simple settings, before developing these ideas to more complex settings and to describe different flows. Comparison with more advanced rheological modelling will be undertaken using numerical simulations.The work lies in EPSRC's Mathematical Sciences and Physical Sciences themes, and more specifically in the "Continuum Mechanics" and the "Complex fluids and rheology" areas.