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Gas-liquid interfacial phenomena are discussed. Surface tension and its relation to interfacial pressure jump are discussed, and static and dynamic contact angles are reviewed. Interfacial force balance and the effect of surface tension nonuniformity are then briefly discussed, followed by a discussion of thermocapillary effect and the role of disjoining pressure in thin liquid films. Mass transfer phenomena at a liquid-gas interphase are discussed, including the predictions of kinetic theory for evaporation and condensation of pure substances. Interfacial equilibrium and transport of sparingly soluble gases are discussed. Semi-empirical treatment of interfacial heat and mass transfer, and the application of convective heat and mass transfer coefficients are discussed. Linear instability and interfacial waves are discussed. Rayleigh-Taylor and Kelvin-Helmholtz instabilities, and instability of gaseous jets are then derived and discussed. Waves at the surface of small bubbles and droplets, and the growth of small vapor bubbles surrounded by superheated liquids are reviewed. Seven solved example problems, and 19 end-of-chapter problems are provided.
Countercurrent flow limitation (CCFL), or flooding, is discussed in this chapter. The physical aspects of CCFL are discussed, and precise definition of various terminologies are reviewed. The two most widely correlation methods, namely the methods of Wallis and Tien-Kutateladze, are presented and discussed. CCFL in vertical flow passages is discussed, followed by the discussion of CCFL in horizontal perforated plates, vertical annular and rectangular flow passages, and horizontal and inclined flow passages. The effect of phase change (evaporation or condensation) on CCFL is discussed. Modeling of CCFL in long flow passages based on the solution of separated-flow momentum equations is reviewed. Two solved example problems and eight end-of-chapter problems are provided.
Two-phase flow in mini and microchannels is discussed. Two-phase flow regimes, empirical and semi-mechanistic flow regime maps, and void fraction in minichannels are reviewed; followed by a discussion of flow regimes and void fraction in microchannels, and in thin annular and rectangular-cross section channels. Two-phase pressure drop in small channels is then reviewed and existing models and correlations that have been specifically developed for small flow passages are discussed. The bubble train (Taylor flow) regime is reviewed and discussed in detail, and the relevant predictive theoretical as well as empirical methods are reviewed. These reviewed methods address pressure drop, hydrodynamic parameters, and interfacial mass transfer. Pressure drops caused by flow area changes in minichannels are discussed. Three solved example problems and 15 end-of-chapter problems are provided.
Pressure drop in adiabatic two-phase flow is discussed in this chapter. Pressure drop predictive methods specifically derived for microchannels or flows with phase change are postponed to later relevant chapters. Mathematical derivations to clarify the precise definitions of various pressure drop terms in 1D two-phase flow are presented. Theoretical bases for two-phase multiplier are discussed. Homogeneous flow models are reviewed. The widely-used empirical correlations for frictional pressure drop are reviewed. Theoretical bases for pressure drops caused by flow disturbances are discussed, first for single-phase flow, and then for two-phase flow. Models and empirical correlations for two-phase pressure drop in various flow disturbances are presented. Single and two-phase pressure drop in helicoidally coiled flow passages are discussed and relevant models and correlations are reviewed. Tables summarizing various homogeneous flow models and methods based on Chisholm-Laird approach are provided. Four solved example problems and 26 end-of-chapter problems are provided.
Mechanistic and semi-analytical two-phase flow regime transition models, and interfacial surface area transport models, are discussed in this chapter. The two-phase flow transition models that are reviewed address concurrent upward pipe flow [Taitel et al. (1980), Mishima and Ishii (1984)], near-horizontal pipe flow [Taitel and Dukler (1976)], and inclined tubes [Taitel et al. (1990)]. The theoretical arguments behind the concept of interfacial surface area transport equations, and mathematical derivations leading to the general form of such a transport equation are presented. The transport equation is then simplified to derive tractable differential equations. The one-group interfacial area transport equation, along with a complete set of closure relations, are then presented. The two-group interfacial area transport equations are then presented and discussed, and references are provided for the required closure relations. Three solved example problems and 13 end-of-chapter problems are provided.
Homogeneous, heterogeneous and dropwise condensation are briefly discussed. Thermal resistances in heterogeneous filmwise as well as direct contact condensation are discussed. Analytical solutions for laminar film condensation on vertical and inclined surfaces, and on horizontal cylindrical tubes, are derived starting from Nusselt’s classical solution. Improvements to these classical solutions are described. Empirical correlations for wavy and turbulent film condensation are presented. Condensation in the presence of a noncondensable gas is discussed, and the Couette flow film model is discussed as a useful tool for modeling condensation in the presence of noncondensables. The fog formation phenomenon in the noncondensable-rich vapor-noncondensable boundary layers is discussed and a method for correcting the condensation rate for the effect of fog formation is reviewed. Condensation of a binary vapor mixture is discussed and the method for modeling filmwise condensation of such mixtures based on the Couetter flow film model is discussed. Two solved example problems and nine end-of-chapter problems are provided.