The Thermodynamics of Linear Fluids and Fluid Mixtures

Pekař, Miloslav; Samohýl, Ivan

doi:10.1007/978-3-319-02514-8

Cited by 32 publications

(71 citation statements)

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“…The whole analysis can be easily generalized to nonideal systems after transformation of independent variables in function J ( T , c ) into function J ( T , a ) where a is the vector of activities; this has no effect on the principles and results of the analysis presented here …”

Section: Resultsmentioning

confidence: 99%

“…In other words, the entropic inequality places explicit restrictions on reaction rates expressed as functions of reaction affinities. The latter are introduced through the (molar) chemical potential defined by Equation :

true μ_{α} = M_{α} \partial (ρ f) / \partial ρ_{α}

…”

Section: Theoretical Methodsmentioning

confidence: 99%

“…Due to the permanence of atoms, this space can be decomposed into two orthogonal subspaces. Consequently, the chemical potential vector can also be decomposed into two orthogonal vectors: μ = A + B . Vector A has as its components traditional affinities of (independent) chemical reactions, but with opposite signs, and is therefore called the (chemical) affinity vector; A =( A 1 , A 2 ,…, A R ).…”

Section: Theoretical Methodsmentioning

confidence: 99%

“…In equilibrium, defined as A eq = J eq = 0 , the left‐hand side of Equation (10) is at the minimum. Finally, mathematical conditions for the extreme value of the function give the following inequality:

true \sum_{p = 1}^{R} \sum_{r = 1}^{R} {(\partial J_{r} / \partial A^{p})}_{eq} A^{p} A^{r} \leq 0

…”

Section: Theoretical Methodsmentioning

confidence: 99%

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Thermodynamic Analysis of Chemically Reacting Mixtures and Their Kinetics: Example of a Mixture of Three Isomers

Pekař

2016

ChemPhysChem

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Thermodynamics provides consequences of and restrictions on chemically reacting mixtures, particularly their kinetics, which have not been fully explored. Herein, a comprehensive thermodynamic analysis is illustrated for a reacting mixture of three isomers. The rate equation is first derived on the basis of the results of nonequilibrium continuum thermodynamics of linear fluids, and is then subjected to the requirement of consistency with entropic inequality (the second law). This consistency test involves the correct representation of the reaction rate as a function of affinities. It is shown that entropic inequality restricts the signs or values of coefficients in the constitutive equations for reaction rates/rate constants. The use of reverse rate constants and the identification of thermodynamic and kinetic equilibrium constants are not necessary in this approach. Although the presented thermodynamic analysis works only for independent reactions, the rates of dependent reactions are not excluded from having effects on kinetics. It is shown that the rates of dependent reactions are combined from the rates of independent reactions differently than dependent reactions are combined from independent reactions. The results are compared to the classical mass-action rate equations, and new restrictions on the values of the classical rate constants are derived.

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Section: Resultsmentioning

confidence: 99%

true μ_{α} = M_{α} \partial (ρ f) / \partial ρ_{α}

…”

Section: Theoretical Methodsmentioning

confidence: 99%

Section: Theoretical Methodsmentioning

confidence: 99%

true \sum_{p = 1}^{R} \sum_{r = 1}^{R} {(\partial J_{r} / \partial A^{p})}_{eq} A^{p} A^{r} \leq 0

…”

Section: Theoretical Methodsmentioning

confidence: 99%

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Thermodynamic Analysis of Chemically Reacting Mixtures and Their Kinetics: Example of a Mixture of Three Isomers

Pekař

2016

ChemPhysChem

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“…The described method can easily be used also in non-ideal systems-concentrations should simply be replaced by activities. [5] …”

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confidence: 97%

The Thermodynamic Driving Force for Kinetics in General and Enzyme Kinetics in Particular

Pekař

2015

ChemPhysChem

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The thermodynamic driving force of a reaction is usually taken as the chemical potential difference between products and reactants. The forward and backward reaction rates are then related to this force. This procedure is of very limited validity, as the resulting expression contains no kinetic factor and gives little information on reaction kinetics. The transformation of the reaction rate as a function of concentration (and temperature) into a function of chemical potential should be more properly performed, as illustrated by a simple example of an enzymatic reaction. The proper thermodynamic driving force is the difference between the exponentials of the totaled chemical potentials of reactants and products.

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A thermodynamic framework for heat‐conducting flows of mixtures of two interacting fluids

Málek

Souček

2022

Z Angew Math Mech

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Within the theory of interacting continua, we develop a model for a heat conducting mixture of two interacting fluids described in terms of the densities and the velocities for each fluid and the temperature field for the mixture as a whole. We use a general thermodynamic framework that determines the response of the material from the knowledge of two pieces of information, namely how the material stores the energy and how the entropy is produced. This information is expressed in the form of the constitutive equations for two scalars: the Helmholtz free energy and the entropy production. Additionally, we follow the goal to determine the response of a mixture from a small (minimal) set of material parameters, including shear viscosity, bulk viscosity and heat conductivity associated with the mixture as a whole and the drag coefficient connected with the interaction force between the constituents. The same thermodynamic approach is used to obtain the model when the mixture as a whole responses as an incompressible material. For both the compressible and incompressible mixtures, we investigate three variants stemming from different definitions of the (averaged) velocity associated with the mixture as a whole. We also address the issue of identification of boundary conditions for the individual constituents from the standard boundary conditions formulated in terms of the quantities associated with the mixture as a whole.

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The Thermodynamics of Linear Fluids and Fluid Mixtures

Cited by 32 publications

References 0 publications

Thermodynamic Analysis of Chemically Reacting Mixtures and Their Kinetics: Example of a Mixture of Three Isomers

Thermodynamic Analysis of Chemically Reacting Mixtures and Their Kinetics: Example of a Mixture of Three Isomers

The Thermodynamic Driving Force for Kinetics in General and Enzyme Kinetics in Particular

A thermodynamic framework for heat‐conducting flows of mixtures of two interacting fluids

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