Two-phase regime

Ishii (1977) One-dimensional drift-flux model and constitutive equations for relative motion between phases in various two-phase regimes. AML Report ANL-77-47 Ide H, Matsumura H, Tanaka Y, Fukano T (1997) Flow patterns and frictional pressure drop in gas-liquid two-phase flow in vertical capUlary channels with rectangular cross section, Trans JSME Ser B 63 452-160... 

Latent heat associated with phase change in two-phase transport has a large impact on the temperature distribution and hence must be included in a nonisothermal model in the two-phase regime. The temperature nonuniformity will in turn affect the saturation pressure, condensation/evaporation rate, and hence the liquid water distribution. Under the local interfacial equilibrium between the two phases, which is an excellent approximation in a PEFG, the mass rate of phase change, ihfg, is readily calculated from the liquid continuity equation, namely... 

Fig. 8 Diffusion (D) and thermal diffusion (Dj) coefficient of PDMS/PEMS (16.4/48.1) left) and Soret coefficient right) for different PDMS mass fractions given in the legends. Binodal points mark the intersection with the binodal. The dashed line segments are extrapolations into the two-phase regime. Figures from [100], Copyright (2007) by The American Physical Society...

In the present article, we review recent progress in this subject area. In Sec. 2, we give a short overview on the chemical composition of the low melting salts and ILs. In Sec. 3 we address the problem of the electrolyte solution structure at conditions of low reduced temperature, where phase separations are known to occur. In Sec. 4, we consider experimental and theoretical results concerning the location of the two-phase regime in solutions of ionic fluids. In Sec. 5 we finally review theoretical and experimental results on near-critical behavior of ionic fluids. 

DI and DD interactions considered in FL and WS theory, are essential ingredients for rationalizing the observed conductance behavior near the two-phase regime. Thus one has not to resort to the assumption of charged triple ions which are not seen in simulations [46,47] Pure pairing theories such as DHEb fail at T < 0.08, which is distinctly above criticality. However, it appears that both FL and WS theory overestimate dissociation. 

The first question to be answered by the simulations concerns the existence of the phase transition. The early calculations for the RPM of Stell et al. [58] and Ebeling [59] based on the MSA, other integral equations and the DH theory have indeed indicated the existence of a two-phase regime with an upper... 

The phase envelope of a mixture is analogous to the vapor pressure curve of a pure component. The vapor pressure curve defines temperature and pressure conditions at which a pure component can exist as vapor and liquid at equilibrium. In this two-phase regime only one parameter, the temperature or the pressure, may be varied independently. 

Fig. 40. Schematic description of unstable thermodynamic fluctuations in the two-phase regime of a binary mixture AB at a concentration cb (a) in the unstable regime inside the two branches tp of the spinodal curve and (b) in the metastable regime between the spinodal curve tp and the coexistence curve The local concentration c(r) at a point r = (x. y, z.) in space is schematically plotted against the spatial coordinate x at some time after the quench. In case (a), the concentration variation at three distinct times t, ti, u is indicated. In case (b) a critical droplet is indicated, of diameter 2R , the width of the interfacial regions being the correlation length Note that the concentration profile of the droplet reaches the other branch ini, of the coexistence curve in the droplet center only for weak supersaturations of the mixture, where cb -

FIGURE 20.1-7 Ternary-phase diagram between polymer, solvent, and nonsolvam. The three regions (a), (It), and (c) refer to the two-phase regimes for which precipitation of polymer occurs with the potential for membrane formation. If the local concentration conditions at a point in a precipitating membrane correspond to one of these domains, the resultant local morphology in the membrane at the point will resemble sketches (n), (fr), or (c) in Fig. 20.1-6, respectively. 

Hou et al. [34] studied the synthesis of dimethyl carbonate from methanol and CO2 as both solvent and reactant, with a methyl iodide promoter. They foimd that as the conversion increased, the mixture critical temperature and pressure increased. Thus, in order to maintain a single-phase mixture, the pressure needed to be increased or correctly chosen a priori. They also foimd that pressure affected the conversion differently, depending on whether the reaction was performed in a single phase or in a vapor-liquid regime. In a two-phase regime, an increase in pressure slightly increased the conversion, while the opposite was true in a single-phase mixture. 

The situation when the flux of liquid water constitutes a significant part of the total water flux in the backing layer is more difficult. This is a true two-phase regime of cell operation, which is not described by this model but is considered in Promislow s work of Chapter 7 of this book. 

There is no phase change in the dry regime, and the phase change in the two-phase regime, outside of the evaporative layer, is 0(f). The Uquid volume fraction jumps from /3, to 0 across the sub-layer. 

In the two-phase regime, the liquid water is everywhere greater than the immobile volume fraction, / , and the gas is saturated to leading order. As in the dry regime, the scaled variables = (C, T, C, Cj,y8 ) describe variations from the channel values, except for the scaled water vapor and water volume fractions, which describe variations from the saturation pressure and the immobile volume fraction, respectively. 

We drop Cj from the leading order adiabatic equations in the two-phase regime. We introduee the liquid potential = 2/3(yS ), obtaining a redueed 4x4 system for the reduced wet variables P = (C, T, ... 

From Eq. (2-109) it can be seen that the tray efficiency g , with no or very poor liquid mixing, is always larger than the point efficiency Eg. A connection between plug flow and ideal mixing in the two phase regime... 

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