Developing two-phase

Zhao and Rezkallah (1993), Rezkallah (1996), and more recently Lowe and Rezkallah (1999) developed two-phase flow transition models for micro-gravity channel flows based on liquid and gas Weber numbers. Zhao and Rezkallah (1993) suggested Wees 1 as the upper boundary for the surface tension-dominated zone, and Wees 20 as the lower boundary for the inertia-dominated zone. 

St. Pierre, C. C., and S. G. Bankoff, 1967, Vapor Volume Profiles in Developing Two-Phase Flow, Int. J. Heat Mass Transfer 10 231. (3)... 

The microstructure of the decomposed Fe-Mo alloy, Fig. 18.136, shows strong alignment of the developing two-phase microstructure along (100) directions. Such alignment is common in cubic crystals, and it arises from the anisotropy of the effective modulus, Y, in the diffusion equation. From Eq. 18.74 it is apparent that the crystallographic directions in which Y is a minimum will correspond to the wavevector of the fastest-growing waves. 

Extensive experimental determinations of overall heat transfer coefficients over packed reactor tubes suitable for selective oxidation are presented. The scope of the experiments covers the effects of tube diameter, coolant temperature, air mass velocity, packing size, shape and thermal conductivity. Various predictive models of heat transfer in packed beds are tested with the data. The best results (to within 10%) are obtained from a recently developed two-phase continuum model, incorporating combined conduction, convection and radiation, the latter being found to be significant under commercial operating conditions. 

Matsen, J. M. Mechanisms of choking and entrainment, Powder Technology 32,21-33 (1982). Militzer, J. Numerical prediction of the fully developed two-phase (air-solids) flow in a pipe, in Circulating Fluidized Bed Technology (P. Basu, ed.), pp. 173-184. Pergamon Press, 1986. 

This hypothesis can be confirmed with a simple engineering model for developed two-phase flow By applying this model to a dilute riser system, the velocity profiles indeed become sharper due to solids and it was found that the most important parameters are solids fraction (see Figure /) and solids diameter. Another important reported fact concerning the hydrodynamics is that the slip velocity can be much higher than the terminal velocity of the particles under consideration. This can be attributed to the presence of clusters... 

Solution flows with high velocity through the long evaporation tubes from bottom to top whilst solvent evaporates. In the top section of the tubes liquid is dragged along as a thin film by the vapor, thus a fully developed two phase flow with a good heat transfer is obtained. Z 4-9 m, = 20- ca. 50 mm, A 100-900 m, 800-2000 mm [0.6], to calculate... 

Nowadays, numerous methods for the quantitative analysis of systems containing surfactants have been developed two-phase titration, UV-vis spectroscopy, gravimetry, to name only a few [4]. However, most of them are rather prolonged and laborious moreover, these methods often do not permit the determination of the individual surfactant content in mixed-surfactant solutions. 

The subroutine is well suited to the typical problems of liquid-liquid separation calculations wehre good estimates of equilibrium phase compositions are not available. However, if very good initial estimates of conjugate-phase compositions are available h. priori, more effective procedures, with second-order convergence, can probably be developed for special applications such as tracing the entire boundary of a two-phase region. 

In addition, the separator temperature and pressure of the surface facilities are typically outside the two-phase envelope, so that no liquids form during separation. This makes the prediction of the produced fluids during development very simple, and gas sales contracts can be agreed with the confidence that the fluid composition will remain constant during field life in the case of a dry gas. 

The free energy of a monolayer domain in the coexistence region of a phase transition can be described as a balance between the dipolar electrostatic energy and the line tension between the two phases. Following the development of McConnell [168], a monolayer having n circular noninteracting domains of radius R has a free energy... 

When two or more phases, e.g. gas, liquid or solid, are in equilibrium, the principles of internal equilibrium developed in section A2.1.5.2 apply. If transfers between two phases a and p can take place, the appropriate potentials must be equal, even though densities and other properties can be quite different. 

Shorthand Notation for Electrochemical Cells Although Figure 11.5 provides a useful picture of an electrochemical cell, it does not provide a convenient representation. A more useful representation is a shorthand, or schematic, notation that uses symbols to indicate the different phases present in the electrochemical cell, as well as the composition of each phase. A vertical slash ( ) indicates a phase boundary where a potential develops, and a comma (,) separates species in the same phase, or two phases where no potential develops. Shorthand cell notations begin with the anode and continue to the cathode. The electrochemical cell in Figure 11.5, for example, is described in shorthand notation as... 

The first point in developing the thermodynamic method is the observation that for equilbrium between two phases-say, a and 3-the chemical potential must be equal in both phases for all components ... 

A widely used type of pump—mixer—settler, developed by IsraeH Mining Industries (IMI) (115), is shown in Figure 13a. A unit having capacity 8.3 m /min (2000 gal /min) has been used in phosphoric acid plants (116). The unique feature of this design is that the pumping device is not required to act as the mixer, and the two phases are dispersed by a separate impeller mounted on a shaft miming coaxially with the drive to the pump. 

The depressed prices of most metals in world markets in the 1980s and early 1990s have slowed the development of new metal extraction processes, although the search for improved extractants continues. There is a growing interest in the use of extraction for recovery of metals from effluent streams, for example the wastes from pickling plants and electroplating (qv) plants (276). Recovery of metals from Hquid effluent has been reviewed (277), and an AM-MAR concept for metal waste recovery has recentiy been reported (278). Possible appHcations exist in this area for Hquid membrane extraction (88) as weU as conventional extraction. Other schemes proposed for effluent treatment are a wetted fiber extraction process (279) and the use of two-phase aqueous extraction (280). 

Filtration is the separation of two phases, particulate form, ie, soHd particles or Hquid droplets, and continuous, ie, Hquid or gas, from a mixture by passing the mixture through a porous medium. This article discusses the more predominant separation of soHds from Hquids. Filtration of soHd particles or Hquid droplets from gases is dealt with elsewhere (see Airpollution controlmethods). The oldest recorded appHcations of filtration are the purifications of wine and water practiced by the ancient Greeks and Romans. Cake filters, such as the rotary vacuum filter and the filter press, were developed much later from the necessity to filter sewage. 

Because almost any diacid can be leaddy converted to the acid chloride, this reaction is quite versatile and several variations have been developed. In the interfacial polymerization method the reaction occurs at the boundary of two phases one contains a solution of the acid chloride in a water-immiscible solvent and the other is a solution of the diamine in water with an inorganic base and a surfactant (48). In the solution method, only one phase is present, which contains a solution of the diamine and diacid chloride. An organic base is added as an acceptor for the hydrogen chloride produced in the reaction (49). Following any of these methods of preparation, the polymer is exposed to water and the acid chloride end is converted to a carboxyhc acid end. However, it is very difficult to remove all traces of chloride from the polymer, even with repeated washings with a strong base. 

A two-phase process developed by CDTech in the 1980s (22,23) and Hcensed also by ABB Lummus Crest is claimed to be appHcable to dilute... 

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