Pushing the limits of generalized Newtonian fluid constitutive equations

高度复杂的非牛顿流体行为在许多工业环境中发挥作用。准确地捕捉这种行为是极具挑战性的。这个博士项目探索了如何使用一个相对简单的“广义牛顿”框架来捕捉复杂的流变行为，包括所谓的“正常应力差”，这通常与复杂的粘弹性、框架不变结构有关。特别是，该项目将探索和分析各向异性粘度张量可以用来捕捉这种行为的方式。该项目将首先探索如何在简单环境中以适当的不变方式制定张量粘度，以捕获各向异性效应，然后将这些想法发展到更复杂的环境中，并描述不同的流动。将使用数值模拟与更先进的流变模型进行比较。这项工作涉及EPSRC的数学科学和物理科学主题，更具体地说，是在“连续介质力学”和“复杂流体和流变学”领域。

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.