Abstract
The development of analytical methods for viscoelastic fluid flows is challenging. Currently, this problem has been solved for particular cases of multimode differential rheological equations of media state (Giesekus, the exponential form of Phan-Tien-Tanner, eXtended Pom-Pom). We propose a parametric method that yields solutions without additional assumptions. The method is based on the parametric representation of the unknown velocity functions and the stress tensor components as a function of coordinate. Experimental flow visualization based on the SIV (smoke image velocimetry) method was carried out to confirm the obtained results. Compared to the Giesekus model, the experimental data are best predicted by the eXtended Pom-Pom model.
Highlights
Nonlinear differential rheological equations of state are being used increasingly often to describe the rheological properties of viscoelastic fluids and to solve fluid mechanics problems related to polymer melts and solutions
Most of the studies deal with unimodal viscoelastic rheological models, e.g., Gruz and Pinho [1,2] (Poiseuille-Couette flows of PTT fluids), Oliveira [3] (Fene-P and Giesekus fluid flows in round pipes and flat channels), Schleiniger and Weinacht [4], or a number of works by Oliveira et al [5] and Coelho et al [6,7], Hashemabadi [9,10]
Our proposed parametric method for multimode Giesekus fluid flows rem ble in a wide range of Weissenberg numbers, but the velocity profiles predicted model are slightly higher than the experimental data in the central region of the
Summary
Nonlinear differential rheological equations of state are being used increasingly often to describe the rheological properties of viscoelastic fluids and to solve fluid mechanics problems related to polymer melts and solutions. The rheological properties of polymeric melts and concentrated polymer solutions are very often more complex than predicted by such unimodal models, and multimode models providing more adequate description are required. In [11], an analytical solution was obtained for a simplified multimode rheological model of a PTT fluid flow. The disadvantage of the numerical approach to solution of the considered problems is that for each particular case, it is necessary to perform a full complex of numerical studies, which, due to strong nonlinearity of the considered equations, requires significant computational resources. The parametric representation of solution yields distributions of velocities and stresses for a wide variety of problems with any degree of accuracy
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