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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
TL;DR: 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.

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Citations
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Journal ArticleDOI
TL;DR: In this article, a set of model equations of active deformable particles including the effect of a general external flow is introduced, and the dynamics under two specific flow profiles is discussed: a linear shear flow, as the simplest example, and a swirl flow.
Abstract: In most practical situations, active particles are affected by their environment, for example, by a chemical concentration gradient, light intensity, gravity, or confinement. In particular, the effect of an external flow field is important for particles swimming in a solvent fluid. For deformable active particles such as self-propelled liquid droplets and active vesicles, as well as microorganisms such as euglenas and neutrophils, a general description has been developed by focusing on shape deformation. In this review, we present our recent studies concerning the dynamics of a single active deformable particle under an external flow field. First, a set of model equations of active deformable particles including the effect of a general external flow is introduced. Then, the dynamics under two specific flow profiles is discussed: a linear shear flow, as the simplest example, and a swirl flow. In the latter case, the scattering dynamics of the active deformable particles by the swirl flow is also considered.

4 citations

Journal ArticleDOI
TL;DR: The derivation of the macroscopic equations for uniaxial polar nematic gels and elastomers is presented and static and dissipative dynamic cross-couplings between strain fields and relative rotations are found that allow for new possibilities to manipulate polar nematics.
Abstract: We present the derivation of the macroscopic equations for uniaxial polar nematic gels and elastomers. We include the strain field as well as relative rotations as independent dynamic macroscopic degrees of freedom. As a consequence, special emphasis is laid on possible static and dynamic cross-couplings between these macroscopic degrees of freedom associated with the network, and the other macroscopic degrees of freedom including reorientations of the macroscopic polarization. In particular, we find static and dissipative dynamic cross-couplings between strain fields and relative rotations on one hand and the macroscopic polarization on the other that allow for new possibilities to manipulate polar nematics. To give one example each for the effects of a static and a dissipative cross-coupling: we find that a static electric field applied perpendicularly to the polar preferred direction leads to relative rotations while dynamically relative rotations can lead to transverse electric currents. In addition to a permanent network, we also consider the effect of a transient network, which is particularly important for the case of gels, melts and concentrated polymer solutions. A section on the influence of macroscopic chirality is included as well.

3 citations

Posted Content
TL;DR: In this article, a unified, densely correlated understanding of granular physics emerges as a result of these phenomena ordered and explained employing a single framework, which is a continuum mechanical theory constructed to qualitatively explain granular phenomena.
Abstract: {\sc gsh} is a continuum mechanical theory constructed to qualitatively account for a broad range of granular phenomena. To probe and demonstrate its width, simple solutions of {\sc gsh} are related to granular phenomena and constitutive models, including (i) for vanishing shear rates: static stress distribution and propagation of elastic waves; (ii) at slow rates: critical state, shear band, the models of hypoplasticity and barodesy; (iii) at higher rates: the MIDI-model, rapid dense flow in the Bagnold regime. A unified, densely correlated understanding of granular physics emerges as a result of these phenomena ordered and explained employing a single framework.

3 citations

Journal ArticleDOI
TL;DR: In this paper, the same symbiotic relation exists between GSH and KCR, or Kamrin's non-local constitutive relation, a model that was successfully employed to account for a wide shear band in split bottom cells.
Abstract: Accounting for elasto-plastic motion in granular media, hypoplasticity is a state-of-the-art constitutive model derived from data accumulated over many decades. In contrast, GSH, a hydrodynamic theory, is derived from general principles of physics, with comparatively few inputs from experiments, yet sporting an applicability ranging from static stress distribution via elasto-plastic motion to fast dense flow, including non-uniform ones such as a shear band. Comparing both theories, we find great similarities for uniform, slow, elasto-plastic motion. We also find that proportional paths and the Goldscheider rule used to construct barodesy, another, more recent constitutive model, are natural results of GSH's equations. This is useful as it gives these constitutive relations a solid foundation in physics, and in reverse, GSH a robust connection to reality. The same symbiotic relation exists between GSH and KCR, or Kamrin's non-local constitutive relation, a model that was successfully employed to account for a wide shear band in split bottom cells.

2 citations

References
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Book
01 Jan 1977

5,094 citations

Book ChapterDOI
01 Jan 1965

3,029 citations

Book
01 Jan 1992
TL;DR: A theory aiming to describe their mechanical behavior must take heed of their deformability and represent the definite principles it obeys as mentioned in this paper, which is not the case in modern physics, since it concerns solely the small particles of matter.
Abstract: Matter is commonly found in the form of materials. Analytical mechanics turned its back upon this fact, creating the centrally useful but abstract concepts of the mass point and the rigid body, in which matter manifests itself only through its inertia, independent of its constitution; “modern” physics likewise turns its back, since it concerns solely the small particles of matter, declining to face the problem of how a specimen made up of such particles will behave in the typical circumstances in which we meet it. Materials, however, continue to furnish the masses of matter we see and use from day to day: air, water, earth, flesh, wood, stone, steel, concrete, glass, rubber, ... All are deformable. A theory aiming to describe their mechanical behavior must take heed of their deformability and represent the definite principles it obeys.

2,644 citations


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

  • ...On the other hand, non-Newtonian fluids are believed to show non-universal behavior and a host of different empirical models have been proposed [16–21] to cope with the flow rheology of such substances....

    [...]

  • ...33, 239 (1961); [18] C....

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Book
01 Jan 1980
TL;DR: The Foundations of Statistical Mechanics 7. Equilibrium Statistical Mechanics 8. Order-Disorder Transitions and Renormalization Theory 9. Interacting Fluids 10. Hydrodynamic Processes near Equilbrium 11. Transport Theory 12.
Abstract: 1. Introduction 2. Introduction to Thermodynamics 3. The Thermodynamics of Phase Transitions 4. Elementary Probability Theory and Limit Theorems 5. Stochastic Dynamics and Brownian Motion 6. The Foundations of Statistical Mechanics 7. Equilibrium Statistical Mechanics 8. Order-Disorder Transitions and Renormalization Theory 9. Interacting Fluids 10. Hydrodynamic Processes near Equilbrium 11. Transport Theory 12. Nonequilibrium Phase Transitions Appendices

1,773 citations


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

  • ...It is based on (the Gibbsian formulation of) thermodynamics [6, 7], symmetries and well-founded physical principles [8]....

    [...]

Journal ArticleDOI
TL;DR: The invariant forms of rheological equations of state for a homogeneous continuum, suitable for application to all conditions of motion and stress, are discussed in this article, where the right invariance properties can most readily be recognized if the frame of reference is a co-ordinate system convected with the material.
Abstract: The invariant forms of rheological equations of state for a homogeneous continuum, suitable for application to all conditions of motion and stress, are discussed. The right invariance properties can most readily be recognized if the frame of reference is a co-ordinate system convected with the material, but it is necessary to transform to a fixed frame of reference in order to solve the equations of state simultaneously with the equations of continuity and of motion. An illustration is given of the process of formulating equations of state suitable for universal application, based on non-invariant equations obtained from a simple experiment or structural theory. Anisotropic materials, and materials whose properties depend on previous rheological history, are included within the scope of the paper.

1,714 citations