Nonlinear fluid dynamics description of non-Newtonian fluids
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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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Journal ArticleDOI
A Nonlinear Network Viscoelastic Model
TL;DR: In this paper, a nonlinear constitutive equation for polymer melts and concentrated solutions is derived from a Lodge-Yamamoto type of network theory, where the network junctions are postulated to move nonaffinely in a well-defined manner.
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Microscopic Theory of Superfluid Helium
TL;DR: In this article, a physical and mathematical characterization of Bose condensation is presented in terms of an additional macroscopic quantity, the wave function of the condensed mode, which is defined by microscopic quantities.
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Microscopic theory of linear, entangled polymer chains under rapid deformation including chain stretch and convective constraint release
TL;DR: A refined version of the Doi and Edwards tube model for entangled polymer liquids is presented in this article, which is intended to cover linear chains in the full range of deformation rates from linear to strongly nonlinear flows.
Engineering thermodynamics, 2nd Ed
D.C. Look,H.J. Sauer +1 more
TL;DR: This book covers both basic and advanced topics in principles of thermodynamics, particularly in the area of availability and irreversibility, refrigeration and heat pumps, and current applications of the principles of Thermodynamics also.