Thixotropic pumping in a cylindrical pipe

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 thixo-viscoplastic Houška model and the thixo-viscous 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 generalised-Newtonian fluid. We propose the name "thixotropic pumping" for this novel transport mechanism.