On Diffusive Variants of Some Classical Viscoelastic Rate-Type Models
Mark Dostalík ^{1, a)}, Vít Průša ^{1, b)} and Tomáš Skřivan ^{2, c)
1)} Faculty of Mathematics and Physics, Charles University, Sokolovská 83, Praha 8 – Karlín, CZ 186 75, Czech Republic
²⁾ Institute of Science and Technology Austria, Am Campus 1, Klosterneuburg, A 3400, Austria

^a) dostalik@karlin.mff.cuni.cz
^b) Corresponding author: prusv@karlin.mff.cuni.cz
^c) tomas.skrivan@ist.ac.at

Abstract. We present a thermodynamically based approach to the design of models for viscoelastic fluids with stress diffusion effect. In particular, we show how to add a stress diffusion term to some standard viscoelastic rate-type models (Giesekus, FENE-P, Johnson–Segalman, Phan-Thien–Tanner and Bautista–Manero–Puig) so that the resulting models with the added stress diffusion term are thermodynamically consistent in the sense that they obey the first and the second law of thermodynamics. We point out the potential applications of the provided thermodynamical background in the study of flows of fluids described by the proposed models.