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
We consider the flow of a thixotropic fluid in a uniform cylindrical pipe, driven by an oscillating pressure gradient or a body force. For a variety of rheological models, solutions can be obtained by integrating ordinary rather than partial differential equations: We illustrate this approach for the thixoviscoplastic Houška model and the thixoviscous simplified Moore-Mewis-Wagner model. We present asymptotic results in the limits of small and large Deborah numbers and numerical results for intermediate Deborah numbers. Under asymmetrical "sawtooth" forcing, thixotropy leads to the net transport of fluid along the pipe, even when there would be no net transport of the corresponding generalized-Newtonian fluid. We propose the name "thixotropic pumping" for this transport mechanism.
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