# Continuum thermodynamics of chemically reacting fluid mixtures

@article{Bothe2013ContinuumTO, title={Continuum thermodynamics of chemically reacting fluid mixtures}, author={Dieter Bothe and Wolfgang Dreyer}, journal={Acta Mechanica}, year={2013}, volume={226}, pages={1757-1805} }

We consider viscous, heat-conducting mixtures of molecularly miscible chemical species forming a fluid in which the constituents can undergo chemical reactions. Assuming a common temperature for all components, we derive a closed system of partial mass and partial momentum balances plus a mixture balance of internal energy. This is achieved by careful exploitation of the entropy principle and requires appropriate definitions of absolute temperature and chemical potentials, based on an adequate…

## 99 Citations

### A Thermodynamical Description of Third Grade Fluid Mixtures

- PhysicsJournal of Non-Equilibrium Thermodynamics
- 2022

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…

### Existence analysis of a stationary compressible fluid model for heat-conducting and chemically reacting mixtures

- MathematicsJournal of Mathematical Physics
- 2022

The existence of large-data weak solutions to a steady compressible Navier–Stokes–Fourier system for chemically reacting fluid mixtures is proved. General free energies are considered satisfying some…

### Existence analysis of a stationary compressible fluid model for heat-conducting and chemically reacting mixtures

- Mathematics
- 2020

The existence of large-data weak solutions to a steady compressible Navier– Stokes–Fourier system for chemically reacting fluid mixtures is proved. General free energies are considered satisfying…

### Weakly nonlocal thermodynamics of binary mixtures of Korteweg fluids with two velocities and two temperatures

- PhysicsEuropean Journal of Mechanics - B/Fluids
- 2020

### Global–in–time existence for liquid mixtures subject to a generalised incompressibility constraint

- MathematicsJournal of Mathematical Analysis and Applications
- 2021

### A multiscale thermodynamic generalization of Maxwell-Stefan diffusion equations and of the dusty gas model

- PhysicsInternational Journal of Heat and Mass Transfer
- 2022

### Thermodynamical analysis and constitutive equations for a mixture of viscous Korteweg fluids

- PhysicsPhysics of Fluids
- 2021

A complete thermodynamical analysis for a binary mixture of viscous Korteweg fluids with two velocities and two temperatures is developed. The constitutive functions are allowed to depend on the…

### Thermodynamic Analysis of Chemically Reacting Mixtures—Comparison of First and Second Order Models

- ChemistryFront. Chem.
- 2018

It is shown that the thermodynamic constraints on the so-called proper rate coefficient are usually simple sign restrictions consistent with the supposed reaction directions, and more freedom in kinetic coupling between reaction steps in a scheme.

### Non-equilibrium diffusion temperatures in mixture of gases via Maxwellian iteration

- Physics
- 2017

This paper studies the difference of non-equilibrium temperatures between constituents, so-called diffusion temperature in the model of mixtures of gases in which each constituent has assigned its…

### On the multi-physics of mass-transfer across fluid interfaces

- Physics
- 2015

Mass transfer of gaseous components from rising bubbles to the ambient liquid can be described based on continuum mechanical sharp-interface balances of mass, momentum and species mass. In this…

## References

SHOWING 1-10 OF 62 REFERENCES

### Variational Theory of Mixtures in Continuum Mechanics

- Physics
- 1990

In continuum mechanics, the equations of motion for mixtures are derived through the use of Hamilton's extended principle which regards the mixture as a collection of distinct continua. The internal…

### The Thermodynamics of Irreversible Processes. II. Fluid Mixtures

- Mathematics
- 1940

The possibility of constructing a systematic theory of irreversible processes is surveyed in general terms, by utilizing some of the results established in later parts of the paper. Three assumptions…

### Thermodynamics and foundations of mass-action kinetics

- Education
- 2005

A critical overview is given of phenomenological thermodynamic approaches to reaction rate equations of the type based on the law of mass-action. The review covers treatments based on classical…

### Instantaneous limits of reversible chemical reactions in presence of macroscopic convection

- Physics
- 2003

### Toward a unified theory of isotropic molecular transport phenomena

- Physics
- 2005

Accurate models for multicomponent transport are a prerequisite for the design of many industrial processes and the interpretation of experiments. Present theories, stemming from the…

### THE MAXWELL-STEFAN FORMULATION OF IRREVERSIBLE THERMODYNAMICS FOR SIMULTANEOUS HEAT AND MASS TRANSFER

- Physics
- 1979

Abstract We consider constitutive relations for diffusion and simultaneous heat conduction in an n-coraponent non-ideal fluid mixture. Using the ideal gas treatment of Hirschfelder, Curtiss and Bird…

### On the thermodynamics of chemically reacting fluid mixtures

- Chemistry, Engineering
- 1971

On the Thermodynamics of Chemically Reacting Fluid Mixtures by Morton E. Gurtin This paper develops a thermodynamical theory of chemically reacting, but inviscid, fluid mixtures. Restrictions placed…

### Dynamics and thermodynamics of complex fluids. I. Development of a general formalism

- Physics
- 1997

We recognize some universal features of macroscopic dynamics describing the approach of a well-established level of description (that is, successfully tested by experimental observations) to…

### Thermodynamics of Irreversible Processes

- Physics
- 1995

This work develops a solution procedure for the kinetic equation for the distribution function of matter in the phase space or the Hilbert space depending on whether the classical or quantum mode of description is adopted for the development of the theory, in a way that the thermodynamics of irreversible processes is described from the molecular viewpoint.