# Application of Kinetic Theory to the Problem of Evaporation and Condensation

TL;DR: In this paper, the motion of a vapor gas in contact with interphase surfaces is studied on the basis of kinetic theory of gases, and the mass and energy fluxes are determined from the condition of the vapor far away from the interfaces.

Abstract: The motion of a vapor gas in contact with interphase surfaces is studied on the basis of kinetic theory of gases. The mass and energy fluxes are determined from the condition of the vapor far away from the interfaces. The result for a vapor gas between two interfaces shows that the temperature gradient in the vapor is opposite in sign to the externally maintained temperature difference.

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TL;DR: In this article, the effect of finite thermal conductivity and recirculation in droplets can be taken into account using the so-called parabolic model, which is a reasonable compromise between accuracy and CPU efficiency.

724 citations

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25 Feb 2008

TL;DR: In this paper, the authors present a general theory of the entropy production for a homogeneous phase and the excess entropy for the Surface Flux Equations and Onsager Relations.

Abstract: General Theory: The Entropy Production for a Homogeneous Phase The Excess Entropy Production for the Surface Flux Equations and Onsager Relations Transport of Heat and Mass Transport of Mass and Charge Applications: Evaporation and Condensation A Non-Isothermal Concentration Cell Adiabatic Electrode Reactions The Formation Cell Modeling the Polymer Electrolyte Fuel Cell The Impedance of an Electrode Surface The Non-Equilibrium Two-Phase van der Waals Model and other chapters.

329 citations

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TL;DR: It is shown how seemingly small simplifications, such as assuming thermal equilibrium across the liquid-vapor interface during evaporation, can lead to the erroneous predictions from the HK relation that have been reported in the literature.

Abstract: Although the Hertz-Knudsen (HK) relation is often used to correlate evaporation data, the relation contains two empirical parameters (the evaporation and condensation coefficients) that have inexplicably been found to span 3 orders of magnitude. Explicit expressions for these coefficients have yet to be determined. This review will examine sources of error in the HK relation that have led to the coefficients’ scatter. Through an examination of theoretical, experimental, and molecular dynamics simulation studies of evaporation, this review will show that the HK relation is incomplete, since it is missing an important physical concept: the coupling between the vapor and liquid phases during evaporation. The review also examines a modified HK relation, obtained from the quantum-mechanically based statistical rate theory (SRT) expression for the evaporation flux and applying a limit to it in which the thermal energy is dominant. Explicit expressions for the evaporation and condensation coefficients are define...

264 citations

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TL;DR: This article analyzes the experimental and the computational simulation data on the droplet evaporation of several different systems and shows that the temperature discontinuity at the liquid-vapour interface discovered by Fang and Ward is a rule rather than an exception and in computer simulations for a single-component system (argon) that this discontinuity is due to the constraint of momentum/pressure equilibrium duringevaporation.

Abstract: Evaporation is ubiquitous in nature. This process influences the climate, the formation of clouds, transpiration in plants, the survival of arctic organisms, the efficiency of car engines, the structure of dried materials and many other phenomena. Recent experiments discovered two novel mechanisms accompanying evaporation: temperature discontinuity at the liquid-vapour interface during evaporation and equilibration of pressures in the whole system during evaporation. None of these effects has been predicted previously by existing theories despite the fact that after 130 years of investigation the theory of evaporation was believed to be mature. These two effects call for reanalysis of existing experimental data and such is the goal of this review. In this article we analyse the experimental and the computational simulation data on the droplet evaporation of several different systems: water into its own vapour, water into the air, diethylene glycol into nitrogen and argon into its own vapour. We show that the temperature discontinuity at the liquid-vapour interface discovered by Fang and Ward (1999 Phys. Rev. E 59 417-28) is a rule rather than an exception. We show in computer simulations for a single-component system (argon) that this discontinuity is due to the constraint of momentum/pressure equilibrium during evaporation. For high vapour pressure the temperature is continuous across the liquid-vapour interface, while for small vapour pressures the temperature is discontinuous. The temperature jump at the interface is inversely proportional to the vapour density close to the interface. We have also found that all analysed data are described by the following equation: da/dt = P(1)/(a + P(2)), where a is the radius of the evaporating droplet, t is time and P(1) and P(2) are two parameters. P(1) = -λΔT/(q(eff)ρ(L)), where λ is the thermal conductivity coefficient in the vapour at the interface, ΔT is the temperature difference between the liquid droplet and the vapour far from the interface, q(eff) is the enthalpy of evaporation per unit mass and ρ(L) is the liquid density. The P(2) parameter is the kinetic correction proportional to the evaporation coefficient. P(2) = 0 only in the absence of temperature discontinuity at the interface. We discuss various models and problems in the determination of the evaporation coefficient and discuss evaporation scenarios in the case of single- and multi-component systems.

252 citations

### Cites background from "Application of Kinetic Theory to th..."

...Fluids 14 1340–6 [16] Pao Y-P 1973 Temperature and density jumps in the kinetic theory of gases and vapors Phys....

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...E 59 417–28 [14] Pao Y-P 1971 Application of kinetic theory to the problem of evaporation and condensation Phys....

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...Fluids 14 306–12 [15] Pao Y-P 1971 Temperature and density jumps in the kinetic theory of gases and vapors Phys....

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TL;DR: In this paper, a theoretical approach based on the transition probability concept of quantum mechanics, called statistical rate theory (SRT), is used to develop an expression for predicting the evaporation flux.

Abstract: Recent measurements of the conditions existing at the interface of an evaporating liquid have found that the temperature approximately one mean free path from the interface in the vapor was higher than the temperature of the liquid at the interface. The measured temperature discontinuity at the interface is in the opposite direction of that predicted by several recent studies based on classical kinetic theory. A theoretical approach based on the transition probability concept of quantum mechanics, called statistical rate theory (SRT), is used herein to develop an expression for predicting the evaporation flux. The expression obtained is free of any fitting parameters. When applied to predict the conditions at which a particular value of the evaporation flux is expected and the result compared with the measurements at 15 different experimental conditions, it is found that the SRT expression accurately predicts the conditions.

188 citations

##### References

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01 Jan 1969

TL;DR: In this paper, the authors present a simulation of a free jet expansion of a high-energy scattering of molecular beams in the presence of high-temperature Viscosity cross sections.

Abstract: Collisional Processes.- Analytical Formulae for Cross Sections and Rate Constants of Elementary Processes in Gases.- Relaxation of Velocity Distribution of Electrons Cooled (Heated) By Rotational Excitation (De-Excitation) Of N2.- Effects of the Initial Molecular States in a High-Energy Scattering of Molecular Beams.- Differential Cross Sections for Ion-Pair Formation with Selection of the Exit Channel.- Low-temperature Viscosity Cross Sections Measured in a Supersonic Argon Beam II.- Excited Oxygen Iodine Kinetic Studies.- Determination of Antisymmetric Mode Energy of CO2 Injected into a Supersonic Nitrogen Flow.- Molecular Beams.- Where are we going with molecular beams?.- Cesium Vapor Jettarget Produced With a Supersonic Nozzle.- Basic Features of the Generation and Diagnostics of Atomic Hydrogen Beams in the Ground and Metastable 22S1/2-States to Determine the Fundamental Physical Constants.- Optical Pumping Of Metastable Neon Atoms in A Weak Magnetic Field.- CO2-Laser Excitation of a Molecular Beam Monitored By Spontaneous Raman Effect.- Time-of-Flight and Electron Beam Fluorescence Diagnostics: Optimal Experimental Designs.- Molecular Beam Time-of-Flight Measurements in A Nearly Freejet Expansion of High Temperature Gas Produced By a Shock Tube.- Electron Beam Diagnostics.- Electron-Beam Diagnostics of High Temperature Rarefied Gas Flows.- Excitation Models Used in the Electron Beam Fluorescence Technique.- Electron - Beam Diagnostics in Nitrogen Multiquantum Rotational Transitions.- Free Jets, Nonequilibrium Expansions.- Free Jet as an Object of Nonequilibrium Processes Investigation.- State Dependent Angular Distributions of Na2 Molecules in a Na/Na2 Free Jet Expansion.- Molecular Beam Time-of-Flight Measurements and Moment Method Calculations of Translational Relaxation in Highly Heated Free Jets of Monatomic Gas Mixtures.- Rovibrational State Population Distributions of CO (v ? 4, J ? 10) In Highly Heated Supersonic Free Jets of CO-N2 Mixtures.- Free Jet Expansion with A Strong Condensation Effect.- Measured Densities in UF6 Free Jets.- Rotational Relaxation of NO in Seeded, Pulsed Nozzle Beams.- The Free-Jet Expansion from a Capillary Source.- Rotational Relaxation in High Temperature Jets of Nitrogen.- Translational Nonequilibrium in a Free Jet Expansion of a Binary Gas Mixture.- Laser Induced Fluorescence Study of Free Jet Expansions.- Jet-Surface Interactions.- Experimental Study of Plume Impingement and Heating Effect on Ariane's Payload.- The Interaction of a Jet Exhausting from a Body with a Supersonic Free Flow of a Rarefied Gas.- Modelling Control Thruster Plume Flow and Impingement.- Impingement of a Supersonic, Underexpanded Rarefied Jet upon a Flat Plate.- Some Peculiarities of Power and Heat Interaction of a Low Density Highly Underexpanded Jet with a Flat Plate.- Condensation in Flows.- Nonequilibrium Condensation in Free Jets.- Condensation and Vapour-Liquid Interaction in a Reflected Shock Region.- Homogeneous and Heterogeneous Condensation of Nitrogen in Transonic Flow.- Investigation of Nonequilibrium Homogeneous Gas Condensation.- The Peculiarities of Condensation Process in Conical Nozzle and in Free Jet Behind it.- Investigation of Nonequilibrium Argon Condensation In Supersonic Jet By Mass-Spectrometry, Electron Diffraction and VUV Emission Spectroscopy.- Clusters and Nucleation Kinetics.- The Microscopic Theory of Clustering and Nucleation.- Kinetics of Cluster Formation and Growth in the Process of Isothermal Condensation.- Relaxation Processes in a Molecular Dynamic Model of Cluster from the Lennard-Jones Particles.- Quantum-Chemical Study Of Processes With Cluster Isomerism.- The Homogeneous Nucleation at the Continuously Changing Temperature and Vapour Concentration.- Molecular Clusters as Heterogeneous Condensation Nuclei.- Experiments with Clusters.- The Photochemistry of Small van der Waals Molecules as Studied by Laser Spectroscopy in Supersonic Free Jets.- Diagnostics of Clusters in Molecular Beams.- Experimental Studies of Water-Aerosol Explosive Vaporization.- Laser Probing of Cluster Formation and Dissociation in Molecular Beams.- Free Molecule Drag on Helium Clusters.- Vibrational Relaxation Kinetics in a Two-Phase Gas-Cluster System.- Gas-Particle Flows.- Long-Range Attraction in the Collisions of Free-Molecular and Transition Regime Aerosol Particles.- Nonequilibrium Statistical Theory of Dispersed Systems.- The Mechanism of Strong Electric Field Effect on the Dispersed Media in the Rarefied Gas.- Generation of High-Speed Aerosol Beams By Laval Nozzles.- Kinetic Model of a Gas Suspension.- Gas Mixtures.- Kinetic Phenomena in the Rarefied Gas Mixtures Flowing Through Channels.- On the Discrete Boltzmann Equation for Binary Gas Mixtures.- Peculiarities and Applicability Conditions of Macroscopic Description of Disparate Molecular Masses Mixture Motion.- Numerical Solution of the Boltzmann Kinetic Equation for the Binary Gas Mixture.- Species Isotope Separation.- Gas or Isotope Separation by Injection into Light Gas Flow.- Molecular Diffusion Through a Fine-Pored Filter Versus Resonante IR-Radiation Intensity.- On Limiting Situations of Gas Dynamic Separation.- A Study of Reverse Leaks.- Investigation of Nonequilibrium Effects in Separation Nozzles by Monte-Carlo Simulation.- Separation of Binary Gas Mixtures at their Effusion through a Capillary and a Nuclear Filler into Vacuum.- Ionized Gases.- Effects of Nonideality in Quantum Kinetic Theory.- Molecular Mass and Heat Transfer of Chemical Equilibrium Multicomponent Partially Ionized Gases in Electromagnetic Field.- Spectroscopic Study of a Plasma Flow along the Stagnation Streamline of a Blunt Body.- On Model Kinetic Operators and Corresponding Langevin Sources for a Non-Equilibrium Plasma.- Related Fields.- Rarefied Gas Dynamics as Related to Controlled Thermonuclear Fusion.- Vacuum Ejectors with Appreciably Uneven Flows in Channels at Low Reynolds Numbers.- Simulation of the Process of the Cosmic Body Formation.

2,747 citations