On the formulation of rheological equations of state

Oldroyd, J. G.

doi:10.1098/rspa.1950.0035

Cited by 1,466 publications

(239 citation statements)

References 4 publications

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“…The Giesekus model is expressed in terms of the upper convected (Oldroyd) time derivative (Oldroyd, 1950;Giesekus, 1984) of the stress tensor, and in compressible form is…”

Section: Reference Model -The Giesekus Modelmentioning

confidence: 99%

On the modelling of highly elastic flows of amorphous thermoplastics

Figiel

Buckley

2009

International Journal of Non-Linear Mechanics

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International audienceTwo approaches to the kinematic structuring of constitutive models for highly elastic flows of polymer melts have been examined systematically, assuming either: (1) additivity of elastic and viscous velocity gradients, or (2) multiplicability of elastic and viscous deformation gradients. A series of constitutive models was compared, with differing kinematic structure but the same linear responses in elastic and viscous limits. They were solved numerically and their predictions compared, and they were also compared to those of the Giesekus model. Several variants, previously proposed as separate models, are shown to be equivalent and qualitatively in agreement with experiment, and therefore a sound basis for construction of models. But the assignment of viscous spin is critical: if it is assumed equal to the total spin with approach (1), or equal to zero with approach (2), then unphysical viscoelastic behaviour is predicted

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“…The Giesekus model is expressed in terms of the upper convected (Oldroyd) time derivative (Oldroyd, 1950;Giesekus, 1984) of the stress tensor, and in compressible form is…”

Section: Reference Model -The Giesekus Modelmentioning

confidence: 99%

On the modelling of highly elastic flows of amorphous thermoplastics

Figiel

Buckley

2009

International Journal of Non-Linear Mechanics

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“…One of the consequences of the theory is that the usual relation between the internal, kinetic and total energies appears as a transformation rule. The derived transformation rule of the energy density, (19), is more general than the usual expression with internal, total and kinetic energies, (6), because of the presence of (self)momentum density. The transformation rules of the physical quantities are transitive.…”

Section: Discussionmentioning

confidence: 99%

“…The principle and also its formulation initiated a long and unfinished discussion among those who are interested in the fundamental aspects of continuum physics. Here we give an incomplete list of the most important looking related works [17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43].…”

Section: Introductionmentioning

confidence: 99%

Galilean relativistic fluid mechanics

Ván

2017

Continuum Mech. Thermodyn.

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Abstract. Single component nonrelativistic dissipative fluids are treated independently of reference frames and flow-frames. First the basic fields and their balances, then the related thermodynamic relations and the entropy production are calculated and the linear constitutive relations are given.The usual basic fields of mass, momentum, energy and their current densities, the heat flux, pressure tensor and diffusion flux are the time-and spacelike components of the third order mass-momentum-energy density-flux four-tensor. The corresponding Galilean transformation rules of the physical quantities are derived.It is proved, that the non-equilibrium thermodynamic frame theory, including the thermostatic Gibbs relation and extensivity condition and also the entropy production is independent of the reference frame and also the flow-frame of the fluid. The continuity-Fourier-Navier-Stokes equations are obtained almost in the traditional form if the flow of the fluid is fixed to the temperature. This choice of the flow-frame is the thermo-flow.A simple consequence of the theory is that the relation between the total, kinetic and internal energies is a Galilean transformation rule.

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“…(u, p) satisfies (14) and (15). In particular, the boundary conditions for the pressure on ∂ω make sense.…”

Section: Theoretical Analysismentioning

confidence: 99%

“…This model is based on a constitutive equation which is an interpolation between purely viscous and purely elastic behaviors, thus introducing a supplementary parameter r which describes the relative proportion of both behaviors (the solvant to solute ratio). Considering the Oldroyd model [15], the momentum, continuity and constitutive equations for an incompressible flow of such a non-Newtonian fluid are, respectively,…”

Section: Introductionmentioning

confidence: 99%

Viscoelastic fluids in a thin domain

Bayada

Chupin

2007

Quart. Appl. Math.

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Abstract. The present paper deals with viscoelastic flows in a thin domain. In particular, we derive and analyse the asymptotic equations of the Stokes-Oldroyd system in thin films (including shear effects). We present a numerical method which solves the corresponding problem and we present some related numerical tests which evidence the effects of the elastic contribution on the flow. Introduction.Much literature has been devoted to the research on non-Newtonian fluids, in a thin film, in both mathematical aspects and applications. It is well known that numerous biological fluids, blood or physiological secretions like tears or synovial fluids, show these non-Newtonian characteristics. In engineering applications people are interested in controling the flows characteristics to suit various requirements such as maintaining the fluid qualities in a wide range of temperatures and stresses. The introduction of additives leads to non-Newtonian behavior of the modern lubricant. Another application domain is linked to polymers, whose non-Newtonian characteristics appear in a wide range of applications such as the molding or injection processes.It is to be noticed that, in most practical applications, the geometry of the flow to be considered is anisotropic. A well-known case deals with the study of boundary layers for complex flows [6,7,14]. Another case, which is the subject of the present paper, is the lubrication problem in which the fluid is contained between two close surfaces in relative motion. These two applications lead to two very different mathematical models, essentially since the order of magnitude of the parameters in the approximation process is different. For example, in the boundary layer study, the Reynolds number is large

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On the formulation of rheological equations of state

Cited by 1,466 publications

References 4 publications

On the modelling of highly elastic flows of amorphous thermoplastics

On the modelling of highly elastic flows of amorphous thermoplastics

Galilean relativistic fluid mechanics

Viscoelastic fluids in a thin domain

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