Non-Newtonian Fluids and the 2nd Law of Thermodynamics

This lecture addresses the peculiar behavior of Non-Newtonian fluids . Particularly the Weissenberg effect in a rotating shear flow is discussed in detail. To this end we consider models of Maxwell-type. In the literature there are three alternatives to describe the evolution of the Non-Newtonian part of the stress by Maxwell-type models . They differ by use of corotational, upper convective and lower convective time derivatives, respectively. We show that solely the classical Maxwell-type model with a corotational time derivative is admissible from a thermodynamic point of view. However, thermodynamics also permits the two other time derivatives but only within a generalized setting, where Maxwell-type models are furnished by supplementary terms . We explicitly provide these new terms and discuss its influence on the High-Weissenberg number problem