Flows with nucleation and condensation

Abstract A survey is presented of recent studies of homogeneous and heterogeneous nucleation and condensation processes and associated flows. The phenomenological (classical) theory of the quasi-steady droplet-formation model with appropriate correction factors can be made to fit homogeneous nucleation and condensation processes in cloud-chamber, supersonic-nozzle and shock-tube flows. Statistical thermodynamics and numerical methods have made it possible to understand small-cluster formation. Free-molecular techniques have contributed significantly to the study of the kinetic processes of clusterization (especially dimerization) and to dynamic properties of small clusters. Heterogeneous nucleation is considered as an extension of the macroscopic theory of homogeneous nucleation. Considerable contributions are expected to the kinetics of heterogeneous condensation from flows in cloud chambers, supersonic nozzles and shock tubes for macroscopic features and from free-molecular-beam techniques for microscopic properties.

[1]  A. Castleman,et al.  The properties of ion clusters and their relationship to heteromolecular nucleation , 1978 .

[2]  G. Stein Angular and Wavelength Dependence of the Light Scattered from a Cloud of Particles Formed by Homogeneous Nucleation , 1969 .

[3]  J. A. Barker,et al.  Theory and Monte Carlo simulation of physical clusters in the imperfect vapor , 1973 .

[4]  J. Hudson,et al.  Condensation in CO2 free jet expansions. II - Growth of small clusters. , 1973 .

[5]  Paul E. Wagner,et al.  The interdependence of droplet growth and concentration. II. experimental test of droplet growth theory , 1975 .

[6]  A. Ziabicki Generalized theory of nucleation kinetics. III. Nucleation in dilute systems and/or in systems with a limited number of effective single elements , 1977 .

[7]  G. Wilemski Binary nucleation. II. Time lags , 1975 .

[8]  J. Kassner,et al.  Homogeneous Nucleation Measurements of Water Vapor in Helium , 1966 .

[9]  F. E. Marble Dynamics of Dusty Gases , 1970 .

[10]  J. Ross,et al.  A stochastic theory of cluster growth in homogeneous nucleation , 1975 .

[11]  G. E. Kelly,et al.  Kinetic Theory of Droplet Growth in Nucleation , 1972 .

[12]  I. I. Glass,et al.  Condensation of water vapor in rarefaction waves. I - Homogeneous nucleation , 1976 .

[13]  J. Katz The critical supersaturations predicted by nucleation theory , 1970 .

[14]  Frank E. Marble,et al.  Some Gasdynamic Problems in the Flow of Condensing Vapors , 1969 .

[15]  F. Abraham,et al.  Erratum: Further Considerations on the Surface Free Energy of Embryonic Droplets in the Nucleation of a Liquid from the Vapor , 1969 .

[16]  E. Rieutord,et al.  Étude de la condensation de vapeur d'eau au cours d'une détente rapide dans un long tube , 1973 .

[17]  R. Etters,et al.  Phase transitions in small clusters of atoms , 1977 .

[18]  J. Calo Dimer formation in supersonic water vapor molecular beams , 1975 .

[19]  R. A. Seban,et al.  The condensation coefficient of water , 1967 .

[20]  W. Courtney Reexamination of homogeneous nucleation and condensation of water , 1968 .

[21]  Joseph Katz,et al.  Condensation of a supersaturated vapor. XII. The homogeneous nucleation of the n‐alkanes , 1970 .

[22]  P. Wegener,et al.  Homogeneous and binary nucleation: new experimental results and comparison with theory , 1976 .

[23]  Evaporation Rates and Lifetimes of Clouds and Sprays in Air. III. The Effects of Cloud Expansion , 1968 .

[24]  Clyde L. Briant,et al.  Molecular dynamics study of the structure and thermodynamic properties of argon microclusters , 1975 .

[25]  J. Fenn,et al.  Clustering of water on hydrated protons in a supersonic free jet expansion , 1974 .

[26]  G. Gyarmathy,et al.  Condensation of air and nitrogen in hypersonic wind tunnels. , 1968 .

[27]  J. L. Katz,et al.  Photoinduced Nucleation of Water Vapor , 1978, Science.

[28]  Dieter Barschdorff,et al.  Verlauf der Zustandsgrößen und gasdynamische Zusammenhänge bei der spontanen Kondensation reinen Wasserdampfes in Lavaldüsen , 1971 .

[29]  P. K. Swaminathan,et al.  Effect of excluded volume on the cluster model of condensation , 1978 .

[30]  K. C. Russell Nucleation on Gaseous Ions , 1969 .

[31]  J. J. Burton The configurational contribution to the free energy of small face centered cubic clusters , 1972 .

[32]  H. Metiu,et al.  Quasithermodynamic treatment of nonuniform systems. I. Adsorption , 1974 .

[33]  J. Zung,et al.  Semiempirical Determination of the Hydrogen Bond Energy for Water Clusters in the Vapor Phase. I. General Theory and Application to the Dimer , 1969 .

[34]  I. Scott,et al.  Dimer Concentrations in Supersonic Free Jets , 1972 .

[35]  D. Mcginty Molecular dynamics studies of the properties of small clusters of argon atoms , 1973 .

[36]  J. Kassner,et al.  The nucleation of water vapor in the absence of particulate matter and ions , 1969 .

[37]  R. Heist,et al.  Homogeneous nucleation in associated vapors. I. Acetic acid , 1976 .

[38]  W. Hillig,et al.  Physical‐Cluster Distributions During Heterophase Fluctuations , 1966 .

[39]  H. Reiss,et al.  Investigation of the homogeneous nucleation of water vapor using a diffusion cloud chamber , 1973 .

[40]  C. Briant,et al.  Effective potential for water‐ion interactions in prenucleation embryos , 1974 .

[41]  C. DeLisi,et al.  A systematic and graphical method for generating the kinetic equations governing the growth of aggregates , 1975 .

[42]  C. Briant,et al.  Molecular dynamics study of the effects of ions on water microclusters , 1976 .

[43]  S. L. Soo,et al.  Fluid dynamics of multiphase systems , 1967 .

[44]  J. Hirth,et al.  Condensation and evaporation : nucleation and growth kinetics , 1963 .

[45]  H. Reiss,et al.  The Use of Nucleation and Growth as a Tool in Chemical Physics , 1977 .

[46]  J. Parlange Free energy of formation of droplets with curvature dependent surface tension , 1970 .

[47]  G. Stein,et al.  Homogeneous nucleation of argon carried in helium in supersonic nozzle flow , 1978 .

[48]  A. Ziabicki Generalized Theory of Nucleation Kinetics. II. Athermal Nucleation Involving Spherical Clusters , 1968 .

[49]  R. P. Andres,et al.  Time Lag in Multistate Kinetics: Nucleation , 1965 .

[50]  A. C. Zettlemoyer,et al.  Homogeneous Nucleation Theory , 1974 .

[51]  J. Katz,et al.  Condensation and boiling: Corrections to homogeneous nucleation theory for nonideal gases , 1973 .

[52]  E. Salpeter Heat transfer in nucleation theory , 1973 .

[53]  L. H. Lund,et al.  Cloud‐Chamber Droplet Growth and Evaporation , 1966 .

[54]  F. Abraham,et al.  On a Generalized Einstein Theory for the Thermodynamics of Planar Surfaces and Microcrystallites , 1971 .

[55]  Danuta Stachórska,et al.  Condensation of Supersaturated Vapor , 1965 .

[56]  Bruce J. Berne,et al.  Computer simulation of the nucleation and thermodynamics of microclusters , 1978 .

[57]  P. Wegener,et al.  Nonequilibrium flow with condensation , 1975 .

[58]  Howard Reiss,et al.  Hydrates in supersaturated binary sulfuric acid‐water vapor , 1974 .

[59]  Wojciech H. Zurek,et al.  Molecular dynamics study of clustering. I , 1978 .

[60]  G. White Steady‐State Random Walks with Application to Homogeneous Nucleation , 1969 .

[61]  A. V. Deursen,et al.  Measurements of intensity and velocity distribution of clusters from a H2 supersonic nozzle beam , 1973 .

[62]  J. Searcy A kinetic model for clustering of water on hydrated protons in a supersonic free jet expansion , 1975 .

[63]  D. R. Forshey,et al.  Condensation of water via rarefaction wave , 1978 .

[64]  G. W. Robinson,et al.  Role of ions in vapor phase nucleation , 1974 .

[65]  W. A. Payne,et al.  Absolute rate constant for the reaction of atomic hydrogen with phosphine over the temperature range 209 to 495 K , 1976 .

[66]  M. Hoare,et al.  Physical cluster mechanics: Statistical thermodynamics and nucleation theory for monatomic systems , 1975 .

[67]  G. Stein,et al.  Condensation of sulfur hexafluoride in steady supersonic nozzle flow , 1978 .

[68]  J. L. Katz,et al.  A kinetic approach to nucleation in condensed systems , 1978 .

[69]  I. Hurle,et al.  Shock-tube Study of the Nucleation of Lead Vapour , 1971, Nature.

[70]  C. Briant,et al.  Molecular dynamics study of water microclusters , 1975 .

[71]  K. Bier,et al.  Homogene Spontankondensation in expandierenden Dampfstrahlen des Kältemittels R 22 bei hohen normierten Drücken , 1977 .

[72]  F. Abraham,et al.  Re‐examination of Homogeneous Nucleation Theory: Statistical Thermodynamics Aspects , 1968 .

[73]  David Jackson McGinty,et al.  Vapor phase homogeneous nucleation and the thermodynamic properties of small clusters of argon atoms , 1971 .

[74]  J. Parlange,et al.  Mayer's Theory of Condensation and Homogeneous Nucleation , 1968 .

[75]  B. G. Schuster,et al.  Homogeneous Nucleation of Water Vapor Determined by Scattering of a Laser Beam , 1966 .

[76]  F. J. Schelling,et al.  Experimental study of nucleation in vapor mixtures of sulfuric acid and water , 1976 .

[77]  E. Salpeter,et al.  Time‐dependent nucleation theory , 1977 .

[78]  H. Frisch,et al.  Time Lag in Nucleation , 1957 .

[79]  J. Bricard,et al.  Experimental study on the nucleation of water vapor sulfuric acid binary system , 1977 .

[80]  P. G. Hill,et al.  Condensation of water vapour during supersonic expansion in nozzles , 1966, Journal of Fluid Mechanics.

[81]  F. Abraham,et al.  A Monte Carlo study of ion–water clusters , 1976 .

[82]  K. Binder Monte Carlo simulation of physical clusters of water molecules , 1975 .

[83]  G. M. Pound,et al.  Statistical mechanics of homogeneous nucleation in vapor , 1977 .

[84]  D. Barschdorff Carrier gas effects on homogeneous nucleation of water vapor in a shock tube , 1975 .

[85]  Yuan-Pern Lee,et al.  Supersonic Molecular Beams of Alkali Dimers , 1971 .

[86]  B. G. Schuster,et al.  Laser scattering measurements of droplet growth in binary mixtures. I. H2O and air , 1973 .

[87]  F. Abraham,et al.  Multistate Kinetics in Nonsteady‐State Nucleation: A Numerical Solution , 1969 .

[88]  D. Stauffer,et al.  Fisher's droplet model and nucleation theory , 1977 .

[89]  S. Loyalka Condensation on a spherical droplet , 1973 .

[90]  J. S. Rathi,et al.  Unsteady Expansion Waveforms Generated by Diaphragm Rupture , 1974 .

[91]  J. Kassner,et al.  New Cloud‐Chamber Method for the Determination of Homogeneous Nucleation Rates , 1965 .

[92]  J. Lothe,et al.  Comments on Homogeneous Nucleation Theory , 1971 .

[93]  H. Reiss Treatment of droplike clusters by means of the classical phase integral in nucleation theory , 1970 .

[94]  G. M. Pound,et al.  Replacement Partition Function for Small Crystals in Homogeneous Nucleation Theory , 1971 .

[95]  F. Stillinger Comment on the Translation–Rotation Paradox in the Theory of Irreversible Condensation , 1968 .

[96]  J. Katz,et al.  Binary homogeneous nucleation as a mechanism for the formation of aerosols , 1974 .

[97]  R. L. Gerlach Kinetics of Nucleation: The Steady State , 1969 .

[98]  C. F. Lee An Experimental Investigation of the Critical Supersaturation of Five Vapors in a Shock Tube , 1978 .

[99]  W. Courtney Kinetics of Condensation of Water Vapor , 1962 .

[100]  R. Cotterill,et al.  Thermodynamics of small clusters of atoms: A molecular dynamics simulation , 1974 .

[101]  E. Clementi,et al.  Study of the structure of molecular complexes , 1976 .

[102]  J. A. Barker,et al.  Physical cluster free energy from liquid‐state perturbation theory , 1974 .

[103]  B. Hale,et al.  Molecular model for ice clusters in a supersaturated vapor , 1974 .

[104]  J. Katz,et al.  Nucleation in associated vapors , 1966 .

[105]  G. Jungclaus,et al.  Berechnung der Strömung in Lavaldüsen mit beliebig verteilter Wärmezufuhr , 1967 .

[106]  L. Loeb On the appearance and mechanisms of formation of langevin-type ions and related nuclei , 1971 .

[107]  C. Briant,et al.  Atomistic models of microclusters; implications for nucleation theory , 1977 .

[108]  H. Reiss,et al.  Theory of vapor phase nucleation in binary mixtures of water and sulfuric acid , 1974 .

[109]  J. Hudson,et al.  Condensation in CO2 free jet expansions. I. Dimer formation , 1973 .

[110]  P. G. Hill,et al.  Nucleation of Supersaturated Vapors in Nozzles. I. H2O and NH3 , 1969 .

[111]  T. Milne,et al.  Detection of Argon Cluster Fragmentation in a Time‐of‐Flight Mass Spectrometer , 1972 .

[112]  L. I. Seleznev,et al.  Generation and growth of condensed phase in high-velocity flows , 1973 .

[113]  L. Smith Experimental investigation of the expansion of moist air around a sharp corner , 1971 .

[114]  P. Plummer,et al.  Molecular Model for Prenucleation Water Clusters , 1972 .

[115]  A. Ziabicki Generalized Theory of Nucleation Kinetics. I. General Formulations , 1968 .

[116]  T. Milne,et al.  Mass‐Spectrometric Observations of Argon Clusters in Nozzle Beams II. The Kinetics of Dimer Growth , 1970 .

[117]  F. Abraham,et al.  Monte Carlo simulation of physical clusters of water molecules , 1974 .

[118]  Georg Gyarmathy,et al.  Zur Wachstumsgeschwindigkeit kleiner Flüssigkeitstropfen in einer übersättigten Atmosphäre , 1963 .

[119]  B. R. De Nucleation of electrically charged droplets , 1979 .

[120]  I. I. Glass,et al.  Condensation of water vapor in rarefaction waves. III - Experimentalresults , 1977 .

[121]  W. Obert,et al.  Cluster Formation in Expanding Supersonic Jets: Effect of Pressure, Temperature, Nozzle Size, and Test Gas , 1972 .

[122]  P. Wagner,et al.  The interdependence of droplet growth and concentration. I. Theory of droplet growth and applications on condensation nuclei counters , 1975 .

[123]  E. Buckle A kinetic theory of cluster formation in the condensation of gases , 1969 .

[124]  P. Plummer,et al.  Theory of Nucleation of Water. I. Properties of Some Clathrate-Like Cluster Structures , 1972 .

[125]  A. I. Rusanov Thermodynamic theory of nucleation on charged particles. , 1979 .

[126]  D. Golomb,et al.  DIMERIZATION IN FREE JETS, FIRST STEP TOWARD CONDENSATION , 1974 .

[127]  J. Katz,et al.  The thermodynamics of cluster formation in nucleation theory , 1972 .

[128]  M. Kasahara,et al.  A kinetic model of sulfuric acid aerosol formation from photochemical oxidation of sulfur dioxide vapor , 1975 .

[129]  E. Knuth Dimer‐formation rate coefficients from measurements of terminal dimer concentrations in free‐jet expansions , 1977 .

[130]  B. J. Mason,et al.  The physics of clouds , 1971 .

[131]  J. Calo,et al.  The calculation of equilibrium mole fractions of polar‐polar, nonpolar‐polar, and ion dimers , 1974 .

[132]  D. R. Forshey,et al.  Homogeneous nucleation of water vapor , 1974 .

[133]  Peter P. Wegener,et al.  Periodic Nozzle Flow with Heat Addition , 1973 .

[134]  R. N. Kortzeborn,et al.  Multistate kinetics in non‐steady‐state nucleation of water on gaseous ions , 1973 .

[135]  J. Hirschfelder Kinetics of homogeneous nucleation on many‐component systems , 1974 .

[136]  G. Stein,et al.  Experiments on the Number of Particles Formed by Homogeneous Nucleation in the Vapor Phase , 1967 .

[137]  F. Abraham,et al.  On the validity of the capillarity approximation in the rate theory of homogeneous nucleation , 1973 .

[138]  P. G. Hill,et al.  Nucleation of Supersaturated Vapors in Nozzles. II. C6H6, CHCl3, CCl3F, and C2H5OH , 1969 .

[139]  G. E. Kelly,et al.  Droplet growth in a dilute vapor , 1974 .

[140]  I. Hurle,et al.  Shock-tube studies on the decomposition of tetramethyl-lead and the formation of lead oxide particles , 1972, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.

[141]  K. Nishioka Thermodynamics of nucleation , 1977 .

[142]  D. Peak Time lag in diffusion‐controlled nucleation , 1978 .

[143]  E. Stoll,et al.  Cluster statistics of the lattice gas model in three and two dimensions , 1976 .

[144]  K. Binder Computer experiments on nucleation processes in the lattice gas model , 1977 .

[145]  P. Mirabel,et al.  Experimental study of nucleation in binary mixtures: The nitric acid–water and sulfuric acid–water systems , 1978 .

[146]  A. M. Sinnarwalla,et al.  Measurement of Growth Rate to Determine Condensation Coefficients for Water Drops Grown on Natural Cloud Nuclei , 1975 .

[147]  E. Clementi,et al.  Study of the structure of molecular complexes. VI. Dimers and small clusters of water molecules in the Hartree‐Fock approximation , 1974 .

[148]  P. Wegener,et al.  Gasdynamics and homogeneous nucleation , 1977 .

[149]  E. R. Cohen The accuracy of the approximations in classical nucleation theory , 1970 .

[150]  G. Wilemski Binary nucleation. I. Theory applied to water–ethanol vapors , 1975 .

[151]  H. R. Byers NUCLEATION IN THE ATMOSPHERE , 1965 .

[152]  A. B. Bailey,et al.  Dimers, Clusters, and Condensation in Free Jets. II , 1972 .

[153]  H. Reiss The replacement free energy in nucleation theory , 1977 .

[154]  J. Fastook,et al.  Water droplet growth in a carbon dioxide atmosphere: A case for small sticking coefficient , 1976 .

[155]  A. Pouring,et al.  Effects of Seeding on the Condensation of Atmospheric Moisture in Nozzles , 1965, Nature.

[156]  R. F. Brown,et al.  Dimers and Clusters in Free Jets of Argon and Nitric Oxide , 1970 .

[157]  J. Gollub,et al.  Laser heterodyne study of water droplet growth , 1974 .

[158]  N. E. Frankel,et al.  Nucleation Theory with a Nonclassical Free Energy , 1971 .

[159]  H. Reiss,et al.  On the composition of nuclei in binary systems , 1976 .

[160]  H. Reiss,et al.  Transient nucleation in H2O–H2SO4 mixtures: A stochastic approach , 1976 .

[161]  K. Schügerl,et al.  Dimers in Supersonic Molecular Beams , 1972 .

[162]  Andrew A. Pouring,et al.  Experiments on Condensation of Water Vapor by Homogeneous Nucleation in Nozzles , 1964 .

[163]  M. R. Hoare,et al.  Statics and Stability of Small Cluster Nuclei , 1971 .

[164]  Andrew A. Pouring,et al.  Thermal Choking and Condensation in Nozzles , 1965 .

[165]  N. Fukuta,et al.  Kinetics of Hydrometeor Growth from a Vapor-Spherical Model , 1970 .

[166]  G. Stein,et al.  Structure of water and carbon dioxide clusters formed via homogeneous nucleation in nozzle beams , 1973 .

[167]  J. Warner,et al.  A Determination of the Condensation Coefficient of Water from the Growth Rate of Small Cloud Droplets , 1974 .

[168]  C. Briant,et al.  A Molecular Model for the Nucleation of Water on Ions , 1976 .

[169]  E. R. Cohen,et al.  Translation-Rotation Paradox in the Theory of Nucleation , 1968 .

[170]  J. Kassner,et al.  Experimental and theoretical study of the sign preference in the nucleation of water vapor , 1971 .

[171]  T. Milne,et al.  Mass Spectrometric Observations of Argon Clusters in Nozzle Beams. I. General Behavior and Equilibrium Dimer Concentrations , 1967 .

[172]  J. Lothe,et al.  Concentration of Clusters in Nucleation and the Classical Phase Integral , 1968 .

[173]  Y. Mori,et al.  A Shock Tube Study on Condensation Kinetics , 1972 .

[174]  Benjamin Wu Possible Water Vapor Condensation in Rocket Exhaust Plumes , 1975 .

[175]  D. A. Sullivan,et al.  On the possibility of complete condensation shock waves in retrograde fluids , 1975, Journal of Fluid Mechanics.

[176]  J. Sislian,et al.  Condensation of water vapour with or without a carrier gas in a shock tube , 1975 .

[177]  B. J. Ostermier,et al.  Diffusion Cloud‐Chamber Investigation of Homogeneous Nucleation , 1967 .

[178]  R. Heist,et al.  Homogeneous nucleation in associated vapors. II. Formic and propanoic acids , 1978 .

[179]  H. Reiss,et al.  Physical clusters in nucleation theory , 1977 .

[180]  F. Abraham,et al.  Thermodynamics of Microcrystallites and Its Relation to Nucleation Theory , 1971 .

[181]  J. J. Burton Free energy of small face centred cubic clusters of atoms , 1973 .

[182]  I. I. Glass,et al.  Comments on ’’Condensation of water via rarefaction wave’’ , 1979 .

[183]  J. Katz,et al.  Condensation of a supersaturated vapor. III. The homogeneous nucleation of CCl4, CHCl3, CCl3F, and C2H2Cl4 , 1976 .

[184]  A. W. Castleman,et al.  Role of Small Clusters in Nucleation about Ions , 1972 .

[185]  H. Reiss,et al.  Physical clusters in an imperfect vapor , 1977 .

[186]  J. Katz,et al.  Resolution of the Translation—Rotation Paradox in the Theory of Irreversible Condensation , 1967 .

[187]  J. Bricard,et al.  Formation of Atmospheric Ultrafine Particles and Ions from Trace Gases , 1977 .

[188]  C. Mou Stochastic theory of phase transition in multiple steady state chemical system: Nucleation , 1978 .

[189]  R. Kikuchi The translation-rotation paradox in the nucleation theory , 1969 .

[190]  Jeong‐long Lin Equilibrium Distribution of Droplets in the Theory of Nucleation , 1968 .

[191]  G. Stein,et al.  Rayleigh scattering experiments on the formation and growth of water clusters nucleated from the vapor phase , 1972 .

[192]  A. Bonissent,et al.  Monte Carlo calculation of the free energy of small monoatomic clusters , 1974 .

[193]  R. Donovan,et al.  Isotope effects in the quenching of electronically excited atoms: Photolysis of CD3I , 1974 .

[194]  J. Lothe,et al.  On the Statistical Mechanics of Nucleation Theory , 1966 .

[195]  B. G. Schuster,et al.  Laser scattering measurements of droplet growth in binary mixtures. II. H2O and argon H2O and helium , 1973 .

[196]  W. J. Dunning,et al.  Homogeneous Nucleation in Steam Nozzle Condensation , 1972 .

[197]  R. Zare,et al.  Internal state distribution of alkali dimers in supersonic nozzle beams , 1973 .

[198]  A. V. Deursen,et al.  Molecular beam intensities and collision cross-sections of small Ne, H2, N2, NO and O2 clusters , 1977 .

[199]  F. Stillinger,et al.  Molecular Dynamics Study of Liquid Water , 1971 .

[200]  O. Hagena Scaling laws for condensation in nozzle flows , 1974 .

[201]  N. Fukuta,et al.  Nonsteady‐state theory of droplet growth , 1973 .

[202]  J. A. Clumpner Light Scattering from Ethyl Alcohol Droplets Formed by Homogeneous Nucleation , 1971 .

[203]  J. Feder,et al.  Homogeneous nucleation and growth of droplets in vapours , 1966 .

[204]  J. J. Burton Configuration, Energy, and Heat Capacity of Small Spherical Clusters of Atoms , 1970 .

[205]  P. Wegener,et al.  Homogeneous Nucleation and Growth of Ethanol Drops in Supersonic Flow , 1972 .

[206]  F. Frank,et al.  On the formulation of microscopic rate equations , 1974 .