Annunziata Palumbo

RHEOLOGICAL PROPERTIES OF DILUTE POLYMER-SOLUTIONS - AN EXTENDED THERMODYNAMIC APPROACH

It is shown that extended irreversible thermodynamics can be used to account for the shear rate and frequency dependences of several material functions like shear viscosity, first and second normal stress coefficients, dynamic viscosity and storage modulus. Comparison with experimental data on steady shearing and small oscillatory shearing flows is performed. A good agreement between the model and experiment is reached in a wide scale of variation of the shear rate and the frequency of oscillations. The relation between the present model which includes quadratic terms in the pressure tensor and the Giesekus model is also examined.

Constitutive Equations for Internal Variables Thermodynamics of Suspensions

Abstract A description of mixtures, including matter diffusion and suspensions, is analyzed from a thermodynamic viewpoint with internal variables. In order to consider dissipative effects due to thermo-diffusion we introduce a set of N independent scalar internal variables, which we denote by γA . The behavior of the mixture is therefore described by a state space W including the classical variables mass density, mass concentration, temperature, and internal variables together with their first and second gradients satisfying evolution equations. General thermodynamic restrictions and residual dissipation inequalities are obtained by the Clausius–Duhem inequality.

Internal Variables Thermodynamics of Two Component Mixtures under Linear Constitutive Hypothesis with an Application to Superfluid Helium

Abstract A model of binary mixtures with an application to superfluid helium is analyzed from a thermodynamical viewpoint with internal variables. Constitutive equations under hypotheses of linearity are obtained.

Thermodynamics of Mixtures as a Problem with Internal Variables. The General Theory

Abstract A model of a mixture with N different components is analyzed from a thermodynamic viewpoint with internal variables, both in the presence and absence of viscosity. Thermodiffusion phenomena are described by N internal variables (N ≥ 2). General thermodynamic restrictions and residual dissipation inequalities are obtained by the Clausius–Duhem inequality.

A mesoscopic thermodynamical description of rheological models

We propose a simple and systematic description of the most used viscoelastic models by using a non-equilibrium thermodynamic approach, generally referred to as the internal variables theory. The main idea is to elevate the conformation tensor

A Thermodynamical Theory with Internal Variables Describing Thermal Effects in Viscous Fluids

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A geometric theory of micropolar mixtures with internal variables

describing the geometrical configuration of the macromolecules to the status of independent variable. It is shown that the sole knowledge of the Helmholtz free energy— whose explicit expression is provided by the kinetic theory—allows to derive the expressions of the polymeric stress tensor and the time evolution equation of the internal variable

A mathematical model for a spatial predator–prey interaction

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Thermodynamics of suspensions of polymeric chains in dilute solutions

, which represents the main ingredients of the rheological models. As illustrations, the Hookean, FENE-P Giesekus, and Bird’s encapsulated dumbbell models are discussed. For completeness, the results are compared with these provided by extended irreversible thermodynamics.

On a model of mixtures with internal variables: Extended Liu procedure for the exploitation of the entropy principle

Abstract In this paper the heat conduction in viscous fluids is described by using the theory of classical irreversible thermodynamics with internal variables. In this theory, the deviation from the local equilibrium is characterized by vectorial internal variables and a generalized entropy current density expressed in terms of so-called current multipliers. Cross effects between heat conduction and viscosity are also considered and some phenomenological generalizations of Fourier’s and Newton’s laws are obtained.