A new constitutive equation derived from network theory

TL;DR: Finite Element Methods for Viscoelastic Fluid Flow Simulations: Formulations and Applications and Applications are presented.

Abstract: The steady motion of a rotating sphere is analysed through two contrasting viscoelastic models, a constant viscosity (FENE-CR) model and a shear-thinning (LPTT) model. Giesekus (Rheol. Acta 9:30–38, 1970) presented an intriguing rotating viscoelastic flow, which to date has not been completely explained. In order to investigate this flow, sets of parameters have been explored to analyse the significant differences introduced with the proposed models, while the momentum-continuity-stress equations are solved through a hybrid finite-element/finite volume numerical scheme. Solutions are discussed for first, sphere angular velocity increase ( $\varOmega$ ), and second, through material velocity-scale increase ( $\alpha$ ). Numerical predictions for different solvent-ratios ( $\beta$ ) show significant differences as the sphere angular velocity increases. It is demonstrated that an emerging equatorial anticlockwise vortex emerges in a specific range of $\varOmega$ . As such, this solution matches closely with the Giesekus experimental findings. Additionally, inside the emerging inertial vortex, a contrasting positive second normal stress-difference ( $N_{2} ( \dot{\gamma} ) = \tau_{rr} - \tau_{\theta\theta}$ ) region is found compared against the negative $N_{2}$ -enveloping layer.

TL;DR: This review explores the tribo-chemical mechanisms underlying astringency in plant-based foods, highlighting the role of salivary protein-polyphenol interactions, lubrication loss, and oral tissue deformation in inducing astringent sensations.

TL;DR: In this article, a nonaffine single-mode rheological model is presented for the steady flow of polymeric melts, and the equations of ηs, Ψ1, λ2, and ηe are derived from the model accordingly.

TL;DR: In this article, the authors derived the stress-strain-time (S − S − T )relation at each instance of macroscopic observations by using the statistical mechanical considerations of equilibrium states.

TL;DR: In this paper, the authors used the continuum theory of anisotropic fluids, as developed by Ericksen and others, to formulate an expression for the time derivative of the end-to-end vector of a linear macromolecule when used in conjunction with the equation describing the distribution function for a dilute solution of dumbbell elements.

TL;DR: In this paper, a model of weak Gaussian networks is used to study the viscosity behavior of concentrated polymer solution. But the model is restricted to the case where the probability of breakage of a chain in the network is independent of elongation of the chain.