Springer Theses

Described by the Square Gradient Model during Evaporation and Condensation

By: Kirill Glavatskiy

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Hardcover | 27 January 2011

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A thermodynamically consistent description of the transport across interfaces in mixtures has for a long time been an open issue. This research clarifies that the interface between a liquid and a vapor in a mixture is in local equilibrium during evaporation and condensation. It implies that the thermodynamics developed for interfaces by Gibbs can be applied also away from equilibrium, which is typically the case in reality. A description of phase transitions is of great importance for the understanding of both natural and industrial processes. For example, it is relevant for the understanding of the increase of CO2 concentration in the atmosphere, or improvements of efficiency in distillation columns. This excellent work of luminescent scientific novelty has brought this area a significant step forward. The systematic documentation of the approach will facilitate further applications of the theoretical framework to important problems.

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Non-Fiction Engineering & Technology Industrial Chemistry & Manufacturing Technologies Industrial Chemistry Chemical Engineering Technology in General Engineering in General Science Chemistry Organic Chemistry Physics Thermodynamics & Heat

Physical Chemistry Mechanical Engineering & Materials Materials Science Engineering Thermodynamics

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Published: 25th February 2013

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Introduction	p. 1
Summary	p. 1
Motivation and Scope	p. 2
Experiments	p. 3
Computer Simulations	p. 3
Theory	p. 4
Multi-Component Systems	p. 5
Structure of the Thesis	p. 6
Nomenclature	p. 6
Overview of the Thesis	p. 8
Non-Equilibrium Thermodynamics of a Surface	p. 9
The Square Gradient Theory	p. 9
Macroscopic Transport	p. 11
References	p. 13
Equilibrium Square Gradient Model	p. 17
Introduction	p. 17
The Gradient Model	p. 18
Gradient Model for the Mass Specific Variables	p. 20
The Lagrange Method	p. 20
Gibbs Relations	p. 22
Equilibrium Surface	p. 24
Gradient Model for the Densities (Per Unit of Volume)	p. 26
Gradient Coefficients	p. 29
Mass and Volume Specific Coefficients	p. 29
Mixing Rules	p. 29
Discussion and Conclusions	p. 30
On the Ambiguity in the Specific Quantities	p. 32
Interfacial Pressure	p. 33
References	p. 35
Non-Equilibrium Continuous Description	p. 37
Introduction	p. 37
The Square Gradient Model	p. 39
The Gibbs Relation	p. 40
Homogeneous Thermodynamics of One-Fluid Mixture	p. 41
Equation of State	p. 42
Helmholtz Energy of a Mixture of Ideal Gases	p. 42
Homogeneous Helmholtz Energy	p. 44
Hydrodynamics of One-Fluid Mixture	p. 45
The Energy Fluxes	p. 46
Two-Dimensional Isotropy of the Surface	p. 47
The Entropy Production	p. 49
The Phenomenological Equations	p. 51
The Force-Flux Relations	p. 51
The Phenomenological Coefficients	p. 53
Discussion and Conclusions	p. 54
On the Extension of the Gibbs Relation to Non-Equilibrium	p. 55
Two-Dimensional Isotropic Components in the 3D Tensorial Quantities	p. 56
References	p. 59
Numerical Solution for the Binary Mixture	p. 61
Introduction	p. 61
Complete Set of Equations	p. 62
Conservation Equations	p. 62
Thermodynamic Equations	p. 62
The Helmholtz Energy of a Homogeneous System	p. 63
The Gradient Contribution	p. 64
Phenomenological Equations	p. 65
Solution Procedure	p. 67
Equilibrium Profile	p. 67
Non-Equilibrium Profile	p. 69
Data Input	p. 72
Results	p. 73
Non-Equilibrium	p. 74
Conclusions	p. 83
References	p. 83
Local Equilibrium of the Gibbs Surface for the Two-Phase Binary Mixture	p. 85
Introduction	p. 85
Equilibrium Gibbs Surface	p. 86
Calculating the Excess Densities	p. 87
Surface Temperature and Chemical Potential Difference	p. 89
Other Surface Quantities	p. 91
Defining Local Equilibrium of a Surface	p. 91
Verification of Local Equilibrium	p. 95
Surface Temperature and Chemical Potential Difference	p. 96
The Non-Equilibrium Gibbs Surface	p. 98
Equilibrium Tables	p. 100
Discussion and Conclusions	p. 102
Excesses' Errors	p. 103
Gibbs Excesses' Relative Errors	p. 104
Equilibrium Table Excesses' Relative Errors	p. 104
References	p. 107
From Continuous to Discontinuous Description	p. 109
Introduction	p. 109
Local Entropy Production	p. 111
Gibbs-Duhem Equation	p. 111
Entropy Balance	p. 112
Excesses in Three-Dimensional Space	p. 113
Definition of an Excess	p. 113
Stationary State of a Surface	p. 114
Excess Entropy Production	p. 116
Surface Transfer Coefficients	p. 117
Gas- and Liquid-Side Transport Coefficients	p. 119
Mass and Molar Transport Coefficients	p. 121
Conclusions	p. 122
On the Definition of an Excess Quantity	p. 122
Excess of a Gradient Function in Curvilinear Coordinates	p. 123
References	p. 124
Surface Transfer Coefficients for the Binary Mixture	p. 127
Introduction	p. 127
Two Component Mixture	p. 127
Methods to Obtain Resistances	p. 129
Perturbation Cell	p. 129
Experiment-Like Procedure	p. 130
Comparison to Kinetic Theory	p. 132
Results	p. 132
Onsager Reciprocal Relations	p. 133
Second Law Consistency	p. 134
Gas- and Liquid-Coefficients	p. 136
Comparison to Kinetic Theory	p. 136
Temperature and Chemical Potential Difference Dependence	p. 138
Discussion and Conclusions	p. 140
References	p. 141
Integral Relations for the Surface Transfer Coefficients	p. 143
Introduction	p. 143
The Entropy Production	p. 144
Stationary States	p. 144
Local Entropy Production	p. 144
Excess Entropy Production	p. 146
Integral Relations	p. 146
Measurable Heat Fluxes	p. 148
The Whole Surface	p. 149
Local Resistivities	p. 149
Results for the Two Component Mixture	p. 151
Integral Relations	p. 151
Numerical Data	p. 153
Discussion and Conclusions	p. 154
Local Resistivities	p. 155
Reference	p. 158
Conclusions and Perspectives	p. 159
This Thesis	p. 159
Perspectives	p. 163
Applications and Extensions	p. 163
Relation to Other Fields	p. 164
References	p. 165
Appendix A Symbols List and Notation Convention	p. 167
Index	p. 171
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Springer Theses

Described by the Square Gradient Model during Evaporation and Condensation

At a Glance

Hardcover

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