Nonlinear fluid dynamics description of non-Newtonian fluids
TLDR
In this paper, a generalized hydrodynamic description of viscoelasticity is presented, which replaces the (often neglected) strain diffusion by a relaxation of the strain as a minimal ingredient, and can be used to get a nonlinear dynamic equation for the stress tensor.Abstract:
Nonlinear hydrodynamic equations for visco-elastic media are discussed. We start from the recently derived fully hydrodynamic nonlinear description of permanent elasticity that utilizes the (Eulerian) strain tensor. The reversible quadratic nonlinearities in the strain tensor dynamics are of the “lower convected” type, unambiguously. Replacing the (often neglected) strain diffusion by a relaxation of the strain as a minimal ingredient, a generalized hydrodynamic description of viscoelasticity is obtained. This can be used to get a nonlinear dynamic equation for the stress tensor (sometimes called constitutive equation) in terms of a power series in the variables. The form of this equation and in particular the form of the nonlinear convective term is not universal but depends on various material parameters. A comparison with existing phenomenological models is given. In particular we discuss how these ad-hoc models fit into the hydrodynamic description and where the various non-Newtonian contributions are coming from.read more
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References
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Comment on "Convective Nonlinearity in Non-Newtonian Fluids" - Temmen et al. Reply
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Lagrange hydrodynamics as extended Euler hydrodynamics: Hamiltonian and GENERIC structures
TL;DR: The extended Euler hydrodynamics proposed in Phys. Rev. Lett. 84 (2000) 3228 as discussed by the authors are interpreted as a reconstruction of Lagrange hyddynamics in the Eulerian setting.
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Modelling rheology and free energy of entangled polymers. State of the art
TL;DR: In this article, the authors present a recent version of the theory that is entirely described by a set of differential equations, and is therefore especially useful for simulations of complex flows as encountered in polymer processing.