The dynamics of a simple model for a thixotropic yield stress fluid. (English) Zbl 1274.76042
Summary: We study the dynamics of a model for thixotropic yield stress fluids which was recently proposed in [M. Renardy, ibid. 165, No. 9-10, 519–526 (2010; Zbl 1274.76062)]. This is based on the partially extended convected model (PEC), modified to allow for a non-zero shear stress limit for large shear rates (PECR), and combined with a Newtonian solvent to enable yielding to homogeneous shear flow (PECR-N) under a prescribed shear stress. We define \(\epsilon\) to be the ratio of retardation time to relaxation time and focus on the limit \(\epsilon\to 0\). Multiple time scales arise and the solutions are investigated with perturbation methods, in conjunction with direct computation of the full set of equations. Both PEC-N and PECR-N capture the experimentally observed phenomenon that the value of yield stress depends on the observation time. For the PECR-N model, we find transient solutions that are not expected from prior work on the PEC-N model, such as blow-up in finite time on the slow manifold, and yielded time-periodic flow.
MSC:
| 76A05 | Non-Newtonian fluids |
Citations:
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