On diffusive variants of some classical viscoelastic rate-type models

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.

Correction of a misprint in the entropy production specification of the Giesekus model

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Cited by in corpus (7)

• Large data existence theory for three-dimensional unsteady flows of rate-type viscoelastic fluids with stress diffusion
• Finite amplitude stability of internal steady flows of the Giesekus viscoelastic rate-type fluid
• Unconditional finite amplitude stability of a viscoelastic fluid in a mechanically isolated vessel with spatially non-uniform wall temperature
• Unconditional finite amplitude stability of a fluid in a mechanically isolated vessel with spatially non-uniform wall temperature
• Implicit type constitutive relations for elastic solids and their use in the development of mathematical models for viscoelastic fluids
• Coupling the Navier-Stokes-Fourier equations with the Johnson-Segalman stress-diffusive viscoelastic model: Global-in-time and large-data analysis
• A thermodynamically consistent Johnson-Segalman-Giesekus model: numerical simulation of the rod climbing effect