| Περίληψη: | Hydrodynamic instabilities are encountered during the motion of non-Newtonian fluids at low flow rates and in the absence of inertia, buoyancy, and surface tension. These unexpected flow configurations, called elastic instabilities, do not arise in the corresponding flows of Newtonian fluids at the same flow rates, and stem from the interaction of the macroscopic flow with the internal microstructure of the complex fluid. Given the plethora of materials that can be classified as complex fluids (polymer solutions and melts, crude oil, blood, foams, emulsions, lava, soft media, etc.), one can envision that such elastic instabilities play a crucial role in the evolution of a wide range of physical, biological and industrial processes. Considering the fact that such elastic instabilities arise at high values of the Weissenberg number (Wi quantifies the level of elasticity in complex fluids), and that current finite element methods cannot reach such values of Wi, because of a notoriously famous numerical instability referred to as the “High Weissenberg Number Problem” (HWNP); we developed a novel finite element formulation that circumvents the HWNP and at the same time yields an extreme reduction in the cost of transient simulations in 2 and 3 dimensions. Using this numerical formalism, we simulated flows of viscoelastic solutions, elasto-visco-plastic materials and entangled polymer melts under conditions that trigger elastic instabilities, which have been observed experimentally but have never been captured theoretically. By means of parametric analysis, we investigated in detail the impact of the rheological properties on the onset criteria of such elastic instabilities. In some cases, we accessed regions of the parameter space where inertial and capillary effects become comparable to elastic effects and studied their interplay on the flow configuration. More specifically, such techniques were employed to: 1) Correlate the presence of certain proteins in human blood plasma with in vitro observed elastic instabilities during its flow, 2) Study the effect of the rheological properties of polymer solutions on the preferential asymmetric passage of the fluid in totally symmetric geometries, 3) Derive experimental protocols for the characterization of the stress-induced transition from solid to liquid state of gels and emulsions under pure extensional deformations, and 4) Investigate the role of the rheological properties of pressure sensitive adhesives on their adhesion energy. Through our analysis, we provided a deeper understanding of the underlying physical mechanisms that cause these elastic instabilities, and aimed at the development of improved, built-to-order materials for various applications.
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