Thermodynamics with Internal Variables. Part II. Applications

Maugin, Gérard A.; Muschik, W.

doi:10.1515/jnet.1994.19.3.250

Cited by 99 publications

(92 citation statements)

References 91 publications

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“…This is the case in the inelastic behavior of solids or in the relaxation effects in thermo-viscous fluids [123,124]. These non-equilibrium parameters, whose nature depends on the phenomenon at hand, are introduced through ordinary differential equations, called kinetic equations, on the basis of physical experiments.…”

Section: Thermodynamics With Internal Variables: the Onsager Proceduresmentioning

confidence: 99%

“…Such an approach leads to more simple systems of equations. Nonetheless, although internal variables are always measurable, in the sense that one can always manage to detect and to measure them [123], they are in general "not controllable", i.e., their value on the boundary cannot be conditioned through the direct action of external forces [123,124]. Hence it is difficult to assign appropriate boundary conditions, [151,152].…”

Section: Comparison Of the Various Approachesmentioning

confidence: 99%

“…Some authors consider CIT with internal variables the real counterpart of EIT and RET [123,124]. In this respect the fluxes are regarded as special extensive internal variables with a kinetic equation in the balance form [123,124].…”

Section: Comparison Of the Various Approachesmentioning

confidence: 99%

“…In this respect the fluxes are regarded as special extensive internal variables with a kinetic equation in the balance form [123,124]. Moreover, internal variables seem to work also for solids, while for these materials is more difficult to develop extended thermodynamics models.…”

Section: Comparison Of the Various Approachesmentioning

confidence: 99%

See 3 more Smart Citations

Entropy Principle and Recent Results in Non-Equilibrium Theories

Cimmelli

Jou

Ruggeri

et al. 2014

Entropy

102

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We present the state of the art on the modern mathematical methods of exploiting the entropy principle in thermomechanics of continuous media. A survey of recent results and conceptual discussions of this topic in some well-known non-equilibrium theories (Classical irreversible thermodynamics CIT, Rational thermodynamics RT, Thermodynamics of irreversible processes TIP, Extended irreversible thermodynamics EIT, Rational Extended thermodynamics RET) is also summarized.

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Section: Thermodynamics With Internal Variables: the Onsager Proceduresmentioning

confidence: 99%

Section: Comparison Of the Various Approachesmentioning

confidence: 99%

Section: Comparison Of the Various Approachesmentioning

confidence: 99%

Section: Comparison Of the Various Approachesmentioning

confidence: 99%

See 2 more Smart Citations

Entropy Principle and Recent Results in Non-Equilibrium Theories

Cimmelli

Jou

Ruggeri

et al. 2014

Entropy

102

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“…Each is briefly described in this section. Other extensions of classical continuum thermodynamics with applications to polymeric liquids are discussed by Maugin and Drouot [70], Stickforth [71], Jou et al [72], Maugin and Muschik [73,74], Drouot and Maugin [75], Muschik et al [76], and Liu [77].…”

Section: Comparison Of Mesoscopic Thermodynamic Theoriesmentioning

confidence: 99%

Theoretical modeling of microstructured liquids: a simple thermodynamic approach

Pasquali

Scriven

2004

Journal of Non-Newtonian Fluid Mechanics

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A new method is presented for accounting for microstructural features of flowing complex fluids at the level of mesoscopic, or coarse-grained, models by ensuring compatibility with macroscopic and continuum thermodynamics and classical transport phenomena. In this method, the microscopic state of the liquid is described by variables that are local expectation values of microscopic features. The hypothesis of local thermodynamic equilibrium is extended to include information on the microscopic state, i.e., the energy of the liquid is assumed to depend on the entropy, specific volume, and microscopic variables. For compatibility with classical transport phenomena, the microscopic variables are taken to be extensive variables (per unit mass or volume), which obey convection-diffusion-generation equations. Restrictions on the constitutive laws of the diffusive fluxes and generation terms are derived by separating dissipation by transport (caused by gradients in the derivatives of the energy with respect to the state variables) and by relaxation (caused by non-equilibrated microscopic processes like polymer chain stretching and orientation), and by applying isotropy. When applied to unentangled, isothermal, non-diffusing polymer solutions, the equations developed according to the new method recover those developed by the Generalized Bracket [J. Non-Newtonian Fluid Mech. 23 (1987) Rheol. 38 (1994) 769]. Minor differences with published results obtained by the Generalized Bracket are found in the equations describing flow coupled to heat and mass transfer in polymer solutions. The new method is applied to entangled polymer solutions and melts in the general case where the rate of generation of entanglements depends nonlinearly on the rate of strain. A link is drawn between the mesoscopic transport equations of entanglements and conformation and the microscopic equation describing the configurational distribution of polymer segment stretch and orientation. Constraints are derived on the generation terms in the transport equations of entanglements and conformation, and the formula for the elastic stress is generalized to account for reversible formation and destruction of entanglements. A simplified version of the transport equation of conformation is presented which includes many previously published constitutive models, separates flow-induced polymer stretching and orientation, yet is simple enough to be useful for developing large-scale computer codes for modeling coupled fluid flow and transport phenomena in two-and three-dimensional domains with complex shapes and free surfaces.

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Weakly nonlocal irreversible thermodynamics

Ván

2003

Ann. Phys.

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Weakly nonlocal thermodynamic theories are critically revisited. A relocalized, irreversible thermodynamic theory of nonlocal phenomena is given, based on a modified form of the entropy current and new kind of internal variables, the so called current multipliers. The treatment is restricted to deal with nonlocality connected to dynamic thermodynamic variables. Several classical equations are derived, including Guyer-Krumhansl, Ginzburg-Landau and Cahn-Hilliard type equations.Comment: 30 pages, no figure

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Thermodynamics with Internal Variables. Part II. Applications

Cited by 99 publications

References 91 publications

Entropy Principle and Recent Results in Non-Equilibrium Theories

Entropy Principle and Recent Results in Non-Equilibrium Theories

Theoretical modeling of microstructured liquids: a simple thermodynamic approach

Weakly nonlocal irreversible thermodynamics

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