In this thesis we study lubrication flows of thixotropic and antithixotropic fluids in two flow problems: unsteady flow in a slowly varying 3D pipe, and oscillating flow in a uniform cylindrical pipe. We consider two fluid models which exhibit interesting non-Newtonian behaviour: the viscous Moore-Mewis-Wagner (MMW) model, and the viscoplastic Houška model. In Chapters 2-6 we study unsteady thixotropic flow in a slowly varying pipe, in a particular regime in which the thixotropic effects are

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... sidered 'weak', with the aim of determining whether we may describe generally the qualitative behaviour of thixotropic fluids in such flows. Previous work by Pritchard et al. [Journal of Non-Newtonian Fluid Mechanics, 238: 140-157, 2016] in the related problem of steady 2D channel flow suggests that such a description may be available. After obtaining the governing equations for this problem, we perform a detailed analysis of the flow for the MMW and Houška models, and determine all of the possible behaviours of these models. This analysis shows that the results and physical interpretations of Pritchard et al. are insightful but not complete. We also study the application of an off-the-shelf finite element program to determine the suitability of such programs for studying slowly varying thixotropic flows. In Chapter 7 we study the similar but simpler problem of unsteady thixotropic pipe flow driven by an oscillating pressure gradient. This problem is simpler than the problem considered in Chapters 2-6, which allows us to explore a wider range of thixotropic behaviours, in which the thixotropic effects range from 'weak' to 'strong'. We are able to describe the full range of thixotropic behaviour using a combination of analytical and numerical methods.