Nonlinear fluid dynamics description of non-Newtonian fluids
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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TL;DR: The relaxation of magnetization, a well-accepted part of ferrofluid dynamics, is shown to give rise to a broad range of non-Newtonian behaviour in ferro-fluid fluids, including shear thinning or shear thickening, normal stress differences, a viscoelastic response and a varying Trouton, or elongational, viscosity.
Abstract: The relaxation of magnetization, a well-accepted part of ferrofluid dynamics, is shown to give rise to a broad range of non-Newtonian behaviour in ferrofluids, including shear thinning or shear thickening, normal stress differences, a viscoelastic response and a varying Trouton, or elongational, viscosity.
30 citations
TL;DR: A generalization of the familiar ferrofluid dynamics by Shliomis is shown capable of realistically accounting for these fluids.
Abstract: The larger magnetic particles in ferrofluids are known to form chains, causing the fluid to display non-Newtonian behavior. In this paper, a generalization of the familiar ferrofluid dynamics by Shliomis is shown capable of realistically accounting for these fluids. The modification consists of identifying the relaxing magnetization as that of the chain-forming particles, while accounting for the free magnetic particles by dissipative terms in the Maxwell equations.
28 citations
TL;DR: The Granular Solid Hydrodynamic (GSH) as discussed by the authors is a unified continuum-mechanical theory for granular media, derived employing the hydrodynamic approach, though as yet a qualitative one.
Abstract: A unified continuum-mechanical theory has been until now lacking for granular media, some believe it could not exist. Derived employing the hydrodynamic approach, Granular Solid Hydrodynamic is such a theory, though as yet a qualitative one. The behavior being accounted for includes static stress distribution, elastic wave, elasto-plastic motion, the critical state and rapid dense flow. The equations and application to a few typical experiments are presented here.
28 citations
TL;DR: In this article, theoretical and numerical results on convection for a magnetic fluid in a viscoelastic carrier liquid were reported. But the results were restricted to the case of idealized boundary conditions and the effect of the Kelvin force and rheology on instability thresholds for diluted suspensions.
27 citations
TL;DR: A unified continuum-mechanical theory has been until now lacking for granular media, some believe it could not exist. as discussed by the authors derived employing the hydrodynamic approach, GSH is such a theory, though as yet a qualitative one.
Abstract: A unified continuum-mechanical theory has been until now lacking for granular media, some believe it could not exist. Derived employing the hydrodynamic approach, GSH is such a theory, though as yet a qualitative one. The behavior being accounted for includes static stress distribution, elastic wave, elasto-plastic motion, the critical state and rapid dense flow. The equations and application to a few typical experiments are presented here.
26 citations
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Book•
01 Jan 1992TL;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....
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...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]....
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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