This book presents the theoretical principles of fog formation. Fundamental formulas are derived for predicting and potentially preventing fog in various practical scenarios. The book reviews basic research on the subject and supports the theoretical findings by comparing them with experimental data.

Since fog formation through homogeneous vapor condensation is possible only in an atmosphere of supersaturated vapor, the book examines the different processes leading to supersaturation in detail. Industrial mists are classified according to the processes responsible for developing supersaturated vapor and are discussed in the respective chapters. The practical application of theoretical techniques for preventing fog formation is covered extensively.

A primary aim of the book is to familiarize readers with methods for assessing the probability of fog formation in different situations and calculating the drop sizes and number densities of mists. The examples provided are largely based on common cases of fog formation encountered in practice.

The focus of this book is on fog condensation, and it does not discuss mist formation by mechanical pulverization and spraying of liquids, as the physical mechanisms for these processes are entirely different.

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PREFACE vii

INTRODUCTION ix

CHAPTER ONE. GENERAL ASPECTS OF FOG CONDENSATION 1
– Supersaturated vapor 1
– Formation of liquid droplets in a gas 2
– Vapor condensation on nuclei 3
– Thermodynamic derivation of Kelvin equation 7
– Homogeneous condensation of vapor 9
– Derivation of the formula for the rate of formation of embryos 9
– New trends in the theory of homogeneous vapor condensation 15
– Critical vapor supersaturation 16
– Methods for the determination of critical supersaturation 17
– Dependence of critical supersaturation on temperature 19
– Condensation nuclei 20
– Experimental data on nucleation rates 24
– Accommodation coefficients 27
– Rate of vapor condensation on the surface of droplets 29
– Temperature of a droplet in supersaturated vapor 31
– Dispersity, number density, and mass concentration of fog 33
– Mechanism of fog formation 35
– References 39

CHAPTER TWO. FORMATION OF SUPERSATURATED VAPOR AND FOG BY ADIABATIC EXPANSION AND RADIATIVE COOLING 43
– Fog formation in an adiabatically expanding vapor-gas mixture 43
– Working formulas for supersaturation 43
– Droplet size and number density of fog 47
– Numerical calculation of fog formation by adiabatic expansion 51
– Cloud chamber and its application 55
– Adiabatic processes in nature and in industry 58
– Fog formation by radiative cooling 58
– References 60

CHAPTER THREE. FORMATION OF SUPERSATURATED VAPOR AND FOG IN TURBULENT MIXING OF GASES 61
– Derivation of working formulas for the supersaturation 61
– Fundamental properties of turbulent jets 72
– Drop size distribution and number density 80
– Rate of nucleation and rate of growth of droplets in a jet 83
– Determination of critical supersaturation in a jet 85
– Various cases of fog formation in turbulent mixing of gases 87
– References 92

CHAPTER FOUR. FORMATION OF SUPERSATURATED VAPOR AND FOG BY MOLECULAR DIFFUSION AND THERMAL CONDUCTION 94
– Derivation of working formulas 94
– The diffusion chamber 98
– Preparation of metal powders 100
– Formation of radiative fogs 101
– References 103

CHAPTER FIVE. FORMATION OF SUPERSATURATED VAPOR AND FOG BY EDDY AND MOLECULAR DIFFUSION AND THERMAL CONDUCTION 105
– Formation of supersaturated vapor during vapor condensation in a pipe 105
– Formation of supersaturated vapor in a turbulent stream between surfaces of different temperature 113
– Formation of supersaturated vapor in the boundary layer 115
– Formation of fog during vapor condensation on a surface 117
– Drop size distribution and number density of fog in pipe condensers 121
– Calculation of drop size distribution and number density of fog forming when H2SO4 vapor condenses in a pipe 127
– Prevention of fog during freezing out of vapor 141
– Prevention of fog during the recovery of volatile solvents by condensation 147
– Prevention of fog during vapor condensation in spray towers 152
– Prevention of fog during vapor condensation in bubblers 163
– References 168

CHAPTER SIX. FORMATION OF SUPERSATURATED VAPOR AND FOG AS THE RESULT OF CHEMICAL REACTIONS OF GASES IN THE VOLUME 170
– Derivation of working formulas for supersaturation 170
– Formation of fog when SO3 is absorbed by aqueous H2SO4 solutions 174
– Photoelectric nephelometry 181
– Formation of condensation nuclei in the atmosphere as the result of chemical reactions of gases in the volume 185
– Production of soot, silica smoke, and Al2O3 powder 187
– Various cases of fog formation as the result of chemical reactions of gases in the volume 195
– References 199

CHAPTER SEVEN. FOGS WITH CONTROLLED NUMBER DENSITY AND DROP SIZE DISTRIBUTION 202
– Drop size and number density as a function of supersaturation 202
– Control of drop size distribution and number density of fogs 206
– Control of drop size in medical aerosols and pesticide sprays 208
– Control of fog dispersity during vapor condensation on the surface 213
– Generation of artificial condensation nuclei and monodisperse fog 216
– References 220