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Journal ArticleDOI

Nonlinear fluid dynamics description of non-Newtonian fluids

17 Apr 2004-Rheologica Acta (D. Steinkopff Verlag.)-Vol. 43, Iss: 5, pp 502-508

AbstractNonlinear 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.

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Journal ArticleDOI
Abstract: A complete continuum mechanical theory for granular media, including explicit expressions for the energy current and the entropy production, is derived and explained. Its underlying notion is: granular media are elastic when at rest, but turn transiently elastic when the grains are agitated—such as by tapping or shearing. The theory includes the true temperature as a variable, and employs in addition a granular temperature to quantify the extent of agitation. A free energy expression is provided that contains the full jamming phase diagram, in the space spanned by pressure, shear stress, density and granular temperature. We refer to the theory as GSH, for granular solid hydrodynamics. In the static limit, it reduces to granular elasticity, shown previously to yield realistic static stress distributions. For steady-state deformations, it is equivalent to hypoplasticity, a state-of-the-art engineering model.

108 citations


Journal ArticleDOI
Abstract: Granular elasticity, an elasticity theory useful for calculating static stress distribution in granular media, is generalized to the dynamic case by including the plastic contribution of the strain. A complete hydrodynamic theory is derived based on the hypothesis that granular medium turns transiently elastic when deformed. This theory includes both the true and the granular temperatures, and employs a free energy expression that encapsulates a full jamming phase diagram, in the space spanned by pressure, shear stress, density and granular temperature. For the special case of stationary granular temperatures, the derived hydrodynamic theory reduces to {\em hypoplasticity}, a state-of-the-art engineering model.

104 citations


Cites background from "Nonlinear fluid dynamics descriptio..."

  • ...Transiently elastic media such as polymers are under active consideration at present [57, 58, 59, 60]....

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  • ...In this equation, the term (uik∇jvk) + (i ↔ j), important for large strain field and frequently negligible for hard grains, is of geometric origin, see [57, 58, 59, 60] for explanations....

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Journal ArticleDOI
TL;DR: This work presents a coherent set of robust tools, in three steps, that enable to formulate elastic, plastic, fluid behaviours in a common, self-consistent modelling using continuous mechanics.
Abstract: Discrete rearranging patterns include cellular patterns, for instance liquid foams, biological tissues, grains in polycrystals; assemblies of particles such as beads, granular materials, colloids, molecules, atoms; and interconnected networks. Such a pattern can be described as a list of links between neighbouring sites. Performing statistics on the links between neighbouring sites yields average quantities (hereafter "tools") as the result of direct measurements on images. These descriptive tools are flexible and suitable for various problems where quantitative measurements are required, whether in two or in three dimensions. Here, we present a coherent set of robust tools, in three steps. First, we revisit the definitions of three existing tools based on the texture matrix. Second, thanks to their more general definition, we embed these three tools in a self-consistent formalism, which includes three additional ones. Third, we show that the six tools together provide a direct correspondence between a small scale, where they quantify the discrete pattern's local distortion and rearrangements, and a large scale, where they help describe a material as a continuous medium. This enables to formulate elastic, plastic, fluid behaviours in a common, self-consistent modelling using continuous mechanics. Experiments, simulations and models can be expressed in the same language and directly compared. As an example, a companion paper (P. Marmottant, C. Raufaste, and F. Graner, this issue, 25 (2008) DOI 10.1140/epje/i2007-10300-7) provides an application to foam plasticity.

93 citations


Journal ArticleDOI
TL;DR: All observations reported to date can be accounted for without invoking the concept of soft elasticity, but instead relying on macroscopic dynamics in the linear and the nonlinear domain.
Abstract: In this short review we give an overview of selected macroscopic properties of sidechain liquid crystalline elastomers (LCEs) focusing on three closely related topics (a) the influence of relative rotations between the director and the strain field on various reorientation instabilities, (b) the nonlinear stress–strain curves for the polydomain–monodomain transition and for the reorientation transition in LCE monodomains and (c) the shear mechanical response of LCEs in the linear regime. We consider only already existing real materials and do not discuss hypothetical “ideal” systems. We conclude that all observations reported to date can be accounted for without invoking the concept of soft elasticity, but instead relying on macroscopic dynamics in the linear and the nonlinear domain.

74 citations


Journal Article
Abstract: In this short review we give an overview of selected macroscopic properties of sidechain liquid crystalline elastomers (LCEs) focusing on three closely related topics (a) the influence of relative rotations between the director and the strain field on various reorientation instabilities, (b) the nonlinear stress-strain curves for the polydomain-monodomain transition and for the reorientation transition in LCE monodomains and (c) the shear mechanical response of LCEs in the linear regime. We consider only already existing real materials and do not discuss hypothetical "ideal" systems. We conclude that all observations reported to date can be accounted for without invoking the concept of soft elasticity, but instead relying on macroscopic dynamics in the linear and the nonlinear domain.

65 citations


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"Nonlinear fluid dynamics descriptio..." refers background in this paper

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Journal ArticleDOI
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