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## Über dieses Buch

This monograph is focused mostly on the exposition of analytical methods for the solution of problems of strong phase change. A new theoretical model is proved useful in describing, with acceptable accuracy, problems of strong evaporation and condensation. The book is the first to treat the problem of asymmetry for evaporation/condensation. A semi-empirical model for the process is proposed for purposes of practical calculation of the process of strong evaporation. The “limiting schemes” of the vapor bubble growth are analyzed. The thermo-hydrodynamic problem of evaporating meniscus of a thin liquid film on a heated surface is considered. A theoretical analysis of the problem of evaporation of a drop levitating over a vapor cushion is performed. The problem of vapor condensation upon a transversal flow around a horizontal cylinder is considered.

The second edition is extended by (i) the conjugate “strong evaporation - heat conduction” problem, (ii) the influence of accommodation coefficients on intensive processes of evaporation and condensation, (iii) the problem of supersonic condensation. This book is the first to present a comprehensive theoretical approach of boiling problems: nucleate boiling, superfluid helium phase transition, similarity between pseudo-boiling and subcritical pressure nucleate boiling. The target audience primarily comprises research experts in the field of thermodynamics and fluid dynamics, but the book may also be beneficial for graduate students.

## Inhaltsverzeichnis

### Chapter 1. Introduction to the Problem

The statistical mechanics (at present, the statistical physics), which is considered as a new trend in theoretical physics and is based on the description of involved systems with infinite number of molecules, was created by Maxwell, Boltzmann, and Gibbs. An important constituent of the statistical mechanics is the kinetic molecular theory, which resides on the Boltzmann integral-differential equation.
Yuri B. Zudin

### Chapter 2. Nonequilibrium Effects on the Phase Interface

The description of intense phase changes calls for the solution to the flow problem in the ambient spaces of evaporating (condensing) matter, as described by gas dynamic equations. The specific feature of an intense phase change lies in the formation near the condensed-phase surface (CPS) of the Knudsen layer of thickness of order of the mean free path of molecules. The existence of the Knudsen layer depends on the nonequilibrium character of evaporation (condensation) resulting in the anisotropy of the velocity distribution function (DF) near CPS. In this setting, the gas dynamic description becomes unjustified—the phenomenological gas parameters (temperature, pressure, density, velocity), as defined according to the conventional rules of statistical averaging, lose their macroscopic sense. Such a situation can be described at a simplified level with the help of an “imaginary experiment”. Assume that the Knudsen layer has hypothetical micrometers of pressure and temperature. Then their readings will not agree with the statistically averaged values, but will rather depend on the structure of a micrometer. Such anomalies disappear beyond the Knudsen layer, in the outer region, where the Navier–Stokes equations hold. The outer region is also called the “Navier–Stokes region”.
Yuri B. Zudin

### Chapter 3. Approximate Kinetic Analysis of Strong Evaporation

The knowledge of the laws governing intense evaporation is important for vacuum technologies, exposure of materials to laser radiation, outflow of a coolant on loss of sealing in the protective envelope of an atomic power plant, and for other applications. The problem of evaporation from a condensed phase surface into a half-space filled with vapor represents a boundary-value problem for the gas dynamics equations.
Yuri B. Zudin

### Chapter 4. Semi-empirical Model of Strong Evaporation

Knowledge of laws of strong evaporation is instrumental for the solution of a number of applied problems: the effect of laser radiation on materials [1], calculation of the parameters of discharge into vacuum of a flashing coolant [2], etc. Strong evaporation also plays an important role in the fundamental problem of simulation of the inner cometary atmosphere. According to the modern view [3], the intensity of icy cometary nucleus varies, as a function of the distance to Sun, in a very substantial range and may reach very large values.
Yuri B. Zudin

### Chapter 5. Approximate Kinetic Analysis of Strong Condensation

In recent years, there has been a growing interest in new fundamental and application problems focused on the study of strong phase transitions like evaporation and condensation. Problems of this kind arise in the study of many processes. In applying laser methods for material treatment it is crucial to know the laws of evaporation process (thermal laser ablation from the target surface) and condensation process (for expanding vapor cloud interacting with the target) [1].
Yuri B. Zudin

### Chapter 6. Linear Kinetic Analysis of Evaporation and Condensation

Nonequilibrium evaporation and condensation are important aspects in numerous fundamental and applied problems. Designing heat screens for space vehicles includes simulating the events of the depressurization of the protection shell of nuclear power units. This problem requires calculation of parameters for strong evaporation of coolant during ejection into vacuum (Larina et al. in Fluid Dyn (1):127−133, 1996 [1]).
Yuri B. Zudin

### Chapter 7. Binary Schemes of Vapor Bubble Growth

In applications related to the physics of boiling, one has to know the dependence of the bubble growth rate at a heated surface on the thermophysical properties of a liquid and vapor, capillary, viscous, and inertial forces, as well as on the kinetic molecular laws operating at an interface [1]. The problem of bubble growth in the rigorous formulation is described by partial differential equations taken separately for a liquid and a vapor phases and supplemented with compatibility conditions at the interface. In the general case, the solution of such multiparametric problem can be only numerical. At the same time, to model the problems of the physics of boiling, approximate analytical solutions for the growth of a bubble are needed to find the general laws governing the influence of various parameters. The basis of the physical modeling of the process of boiling is an idealized problem on a spherically symmetric growth of a vapor bubble in an infinite volume of a uniformly superheated liquid [2].
Yuri B. Zudin

### Chapter 8. Pressure Blocking Effect in a Growing Vapor Bubble

The phenomenon of gas (vapor) bubbles in a liquid, in spite of the fluctuation character of their nucleation and the short lifetime, has a wide spectrum of manifestations: underwater acoustics, sonoluminescence, ultrasonic diagnostics, decreasing friction by surface nanobubbles, nucleate boiling, etc. (Lohse in Nonlinear Phenom Complex Syst 9:125–132, 2006 [1]). Such exotic manifestations of the bubble behavior as a micropiston injection of droplets in jet printing and the spiral rise path of bubbles in a liquid (the Leonardo da Vinci paradox) permitted the authors of (Straub in Adv Heat Transf 35:157–172, 2001) [2] to speak of “bubble puzzles.” The most important application of the bubble dynamics is the effervescence of a liquid superheated with respect to the saturation temperature. The liquid retains thereby the properties of the initial phase but becomes unstable (or metastable). The result of the demonstration of metastability of the liquid is the initiation and growth of nuclei of a new (vapor) phase in it. An ideal subject of investigation of this phenomenon is the spherically asymmetric growth of the vapor bubble in the volume of a uniformly superheated liquid. However, the experimental realization of such a process presents great challenges.
Yuri B. Zudin

### Chapter 9. Evaporating Meniscus on the Interface of Three Phases

Modern progress in the nanotechnology, micro- and nano-electronics depends on a detailed analysis of the behavior of the interphase boundary in microscopic objects, and in particular, on the “liquid-gas” interphase boundary.
Yuri B. Zudin

### Chapter 10. Kinetic Molecular Effects with Spheroidal State

Cooling of a hot surface by dropwise jets is widely useful in various engineering problems: power systems, metallurgy, cryogenic systems.
Yuri B. Zudin

### Chapter 11. Flow Around a Cylinder (Vapor Condensation)

The problem of vapor condensation on a solid surface has been traditionally referred to as a classical problem of two-phase thermohydrodynamics. The best-studied case is the condensation of a steady-state vapor on a vertical plate [1, 2], when the hydrodynamics of the laminar flow of a condensate film is determined by the interaction between the gravity forces (the driving force) and the viscous friction on the wall. The analytical solution to this problem was obtained in 1916 in fundamental studies by Nusselt [3, 4].
Yuri B. Zudin

### Chapter 12. Nucleate Pool Boiling

The first documented mention of superheated liquid occurred in 1777 when the London Royal Society issued a recommendation to place a thermometer bulb not in boiling water itself, but rather in its vapors. In 1873, a century later, Gibbs [1] was first to carry out a physical analysis of specific features of the superheated (“metastable”) state of liquid. Interesting facts about early observations of superheated liquid can be found in “Course in Physics” by Khvolson (1923).
Yuri B. Zudin

### Chapter 13. Heat Transfer in Superfluid Helium

The superfluidity phenomenon of helium, which was discovered in the 1930s by Kapitza (Nature 141:74, 1938) [1], is about 100 years old. The superfluidity, which a macroscopic quantum phenomenon, is related to the formation (“condensation”) of a finite number of particles in one quantum state. This condensate of particles features some properties of the dissipation-free motion, which are responsible for the superfluidity phenomenon (Schmitt in Introduction to superfluidity: field-theoretical approach and applications. Springer, 2004) [2]. Below we shall be concerned only with superfluidity of Helium-4, which is the most common of the two isotopes of helium in nature. The superfluidity of the second isotope (Helium-3), which is a much more involved insufficiently known problem (Audi et al. in Nucl Phys A 729:3–128, 2003) [3], is beyond the scope of this book. So, below by “helium” we shall mean Helium-4. Helium is an extremely unusual system. This inert gas condenses only at a few degrees Kelvin and only helium remains a fluid down to absolute zero $$T = 0$$. Solidification of helium requires pressure about 30 atm. Because of this, the phase diagram for helium does not contain the triple point, which is standard for all other substances. At normal pressure helium boils at 4.2 K, the thermodynamic critical point corresponds to 5.19 K at pressure 2.24 atm. The “reluctance” of helium to form crystals can be explained by quantum effects—because of small mass of atoms and weakness of their interactions, their deflections from the equilibrium position in helium crystal are comparable with the interatomic distance, which leads to the “delocalization” of atoms in the crystal. To a certain extent, the smallness of the amplitude of the zero-point vibrations of atoms in the crystal lattice is analogous to the behavior of electrons in an ordinary metal. A remarkable property of quantum crystals of helium is their ability to generate crystallization waves, which can be looked upon as a dissipationless recrystallization of the surface.
Yuri B. Zudin

### Chapter 14. Concept of Pseudo-Boiling

In the area of pressures above the thermodynamic critical $$\left( {p > p_{c} } \right)$$, pure substances are known to behave like single-phase liquids with locally equilibrium properties. This range of parameters is called the area of supercritical pressures (SCP), and the medium in it, a supercritical fluid (SCF) [1]. The area of supercritical pressures had become the subject of interest in thermal engineering in connection with the attempts to solve the principal problem of enhancing the initial vapor parameters in the 1960s. SCFs are considered as promising coolants due to their specific properties, and at present SCP power units play the key role in heat power engineering of advanced countries.
Yuri B. Zudin

### Chapter 15. Bubbles Dynamics in Liquid

The derivation of the generalized Rayleigh equation that describes the dynamics of a spherical gas bubble in a tube filled with an ideal liquid is given. Its solution has spherical (the classical Rayleigh equation) and cylindrical (the case of a long tube) asymptotics. An exact analytical solution of the problem on vapor bubble collapse in a long tube was obtained.
Yuri B. Zudin

### Backmatter

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