Abstract
A complete thermodynamical analysis for a non-reacting binary mixture exhibiting the features of a third grade fluid is analyzed. The constitutive functions are allowed to depend on the mass density of the mixture and the concentration of one of the constituents, together with their first and second order gradients, on the specific internal energy of the mixture with its first order gradient, and on the symmetric part of the gradient of barycentric velocity. Compatibility with the second law of thermodynamics is investigated by applying the extended Liu procedure. An explicit solution of the set of thermodynamic restrictions is obtained by postulating a suitable form of the constitutive relations for the diffusional mass flux, the heat flux, and the Cauchy stress tensor. Taking a first order expansion in the gradients of the specific entropy, the expression of the entropy flux is determined. It includes an additional contribution due to non-local effects.
Funding source: Gruppo Nazionale per la Fisica Matematica
Funding source: Istituto Nazionale di Alta Matematica ”Francesco Severi”
Funding statement: This work is supported by the Gruppo Nazionale per la Fisica Matematica (GNFM) of the Istituto Nazionale di Alta Matematica “F. Severi.” M. G. acknowledges support through the “Progetto Giovani GNFM 2020.”
Acknowledgment
The authors thank the anonymous referees for the helpful comments leading to clarification of some aspects and improvement of the quality of the paper.
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© 2022 Walter de Gruyter GmbH, Berlin/Boston
Artikel in diesem Heft
- Frontmatter
- Editorial
- Editorial
- Research Articles
- Pattern Formation in Thermal Convective Systems: Spatio-Temporal Thermal Statistics, Emergent Flux, and Local Equilibrium
- A Thermodynamical Description of Third Grade Fluid Mixtures
- A Robust Physics-Based Calculation of Evolving Gas–Liquid Interfaces
- Thermal Shear Waves Induced in Mesoscopic Liquids at Low Frequency Mechanical Deformation
- Sources of Finite Speed Temperature Propagation
- Non-Linear Heat Transport Effects in Systems with Defects
- Nonlinear Thermal Transport with Inertia in Thin Wires: Thermal Fronts and Steady States
- Optimizing the Piston Paths of Stirling Cycle Cryocoolers
- Non-Linear Stability and Non-Equilibrium Thermodynamics—There and Back Again
- Variational Approach to Fluid-Structure Interaction via GENERIC
- Short Communication
- Thermodynamical Foundations of Closed Discrete Non-Equilibrium Systems
- Review
- Thermotics As an Alternative Nonequilibrium Thermodynamic Approach Suitable for Real Thermoanalytical Measurements: A Short Review
Artikel in diesem Heft
- Frontmatter
- Editorial
- Editorial
- Research Articles
- Pattern Formation in Thermal Convective Systems: Spatio-Temporal Thermal Statistics, Emergent Flux, and Local Equilibrium
- A Thermodynamical Description of Third Grade Fluid Mixtures
- A Robust Physics-Based Calculation of Evolving Gas–Liquid Interfaces
- Thermal Shear Waves Induced in Mesoscopic Liquids at Low Frequency Mechanical Deformation
- Sources of Finite Speed Temperature Propagation
- Non-Linear Heat Transport Effects in Systems with Defects
- Nonlinear Thermal Transport with Inertia in Thin Wires: Thermal Fronts and Steady States
- Optimizing the Piston Paths of Stirling Cycle Cryocoolers
- Non-Linear Stability and Non-Equilibrium Thermodynamics—There and Back Again
- Variational Approach to Fluid-Structure Interaction via GENERIC
- Short Communication
- Thermodynamical Foundations of Closed Discrete Non-Equilibrium Systems
- Review
- Thermotics As an Alternative Nonequilibrium Thermodynamic Approach Suitable for Real Thermoanalytical Measurements: A Short Review