MSc Students Presentations - Georgios Makrygiorgos

The well-established feature of the so-called yield stress fluids is the existence of a critical stress value, namely yield-stress, which explicitly dictates the nature of the material based on the applied stresses on it. If the applied stresses do not exceed the aforementioned critical value, the material behaves as a solid medium, whereas it is able to deform like a liquid for higher stresses.  Computation of viscoplastic fluid flows has always been a challenging task and for that reason several modeling or numerical approaches have been proposed, the most popular being the Papanastasiou regularization (PR) and the Augmented Lagrangian (AL) methods, respectively. A fast converging and efficient algorithm is proposed for tracking the yield surface and predicting the flow field of viscoplastic fluids accurately. The numerical procedure is the Penalized Augmented Lagrangian (PAL) method. To test the efficiency of our algorithm, several benchmark flow-problems with fixed, free and moving boundaries are studied.  In all cases, the algorithm captures the yield surfaces correctly, while maintaining a low computational cost. Based on these extensive tests, PAL is found to be superior combining accuracy and speed to all existing solution methods for viscoplastic fluids. Taking advantage of the robustness of the PAL method, extensional flows of Viscoplastic fluids are studied next and, more specifically, the stretching induced breakup of Viscoplastic bridges. Due to the presence of an axial symmetry, the governing equations are solved in 2-D. The code is validated via comparison of our results to a previous numerical study of Balmforth et al. (2010) where the 1-D slender filament approximation had been used, and experiments of the same authors. Subsequently, a parametric analysis is performed for several key characteristic quantities. In addition, we compare our computational results with the experimental data of Niedzwiedz et al. (2010).

All the aforementioned concerned simple Viscoplastic fluids whose modelling follows the simplest approach regarding the true nature of yield stress fluids. In recent years, though, constitutive modelling of yield stress systems has greatly advanced, introducing the ideas of elasticity and flow-dependent variation of the rheological parameters.  This lead to the rheology of Thixotropic Elasto-Visco-Plastic fluids (TEVP),  where phenomena that take place in the microstructure must be accounted for. To this end, we couple the tensorial constitutive model by Saramito (2009) for EVP fluids with Isotropic Hardening (IH) to account for thixotropy and Kinematic Hardening (KH), to account for back-stresses following the earlier work of Dimitriou et al.(2013-2014). The new model is evaluated via examination of simple rheometric flows, including steady and step-shear tests, flow reversal, intermittent step tests, SAOS and LAOS. Our model reproduces these experimental data quantitatively, highlighting its predictive capabilities. We further examined the model in uniaxial elongation and found that it is important to include this particular flow in the rheological characterization of such systems. Apart from simple rheometric tests, we also present the predictions of the model in a wide-gap Taylor Couette configuration.