Unsteady flow of a thixotropic fluid in a slowly varying pipe

We analyse the unsteady axisymmetric flow of a thixotropic or antithixotropic fluid in a slowly varying cylindrical pipe. We derive general perturbation solutions in regimes of small Deborah numbers, in which thixotropic or antithixotropic effects enter as perturbations to generalised Newtonian flow. We present results for the viscous Moore–Mewis–Wagner model and the viscoplastic Houška model, and we use these results to elucidate what can be predicted in general about the behaviour of thixotropic and antithixotropic fluids in lubrication flow. The range of behaviour we identify casts doubt on the efficacy of model reduction approaches that postulate a generic cross-pipe flow structure.