Two-phase fluid system

Consider a two-component, two-phase fluid system. Let (3 be a spherical fluid droplet of radius r surrounded by a, the second fluid phase. The equilibrium conditions are... 

In preparation for our subsequent treatment, we now consider a macroscopic two-phase fluid system with a planar interface of area s separating the bulk phases a and j. For the description of surface phenomena, the concentrations of the various components, p, and the components of the stress tensor d must be specified. In the interior of the bulk phases, the concentrations, be... 

Another model for which (2.1), (2.2) may be applied is the two-phase fluid system without memory which models two-phase equilibria in pure fluid. It has one constituent in two phases which are uniform bodies where the masses and volumes of which are denoted by m and respectively. For the whole volume... 

Heat pipes are generally simple two phase fluid systems in which heat is removed from a source by evaporation, transported to the cooler end of the pipe, and then deposited into the sink by condensation, as shown in Figure 10-8. Some key characteristics of heat pipes... 

Figure A2.5.11. Typical pressure-temperature phase diagrams for a two-component fluid system. The fiill curves are vapour pressure lines for the pure fluids, ending at critical points. The dotted curves are critical lines, while the dashed curves are tliree-phase lines. The dashed horizontal lines are not part of the phase diagram, but indicate constant-pressure paths for the T, x) diagrams in figure A2.5.12. All but the type VI diagrams are predicted by the van der Waals equation for binary mixtures. Adapted from figures in [3].

Barclay, F. J., T. J. Ledwidge, and G. C. Cornfield, 1969, Some Experiments on Sonic Velocity in Two-Phase Critical Flow, Symp. on Fluid Mechanics and Measurements in Two-Phase Flow Systems, Proc. Inst. Mech. Eng. 184(Part 3C) 185-194. (3)... 

Dean, R A., R. S. Dougall, and L. S. Tong, 1971, Effect of Vapor Injection on Critical Heat Flux in a Subcooled R-l 13 (Freon) Flow, Proc. Int. Symp. on Two-Phase Flow Systems, Haifa, Israel. (6) Deane, C. W., and W. M. Rohsenow, 1969, Mechanism and Behavior of Nucleate Boiling Heat Transfer to the Alkali Liquid Metals, USAEC Rep. DSR 76303-65, Massachusetts Institute of Technology, Cambridge, MA Also in 1970, Liquid Metal Heat Transfer and Fluid Dynamics J. C. Chen and A. A. Bishop, Eds., ASME Winter Annual Meeting, New York. (4)... 

Step 3. The Reynolds number Re is calculated in this step. Dukler developed experimental data determining liquid holdup in two-phase flow systems. Re values above 200,000 are free of liquid slugs and holdup. If Re is greater than 200,000, then the flow is in the froth zone, or it is simply homogeneous flow as a mixture. For homogeneous flow, the average density of the two-phase flow fluid mixture is ... 

A boundary layer is formed between the two phases (fluid and solid). This is a stagnant film that represents a layer of less movement of the fluid and hence builds up a zone with resistance to mass transfer. The mass transfer coefficient and generally the mass transfer rate depend on the fluid dynamics of the system. Higher fluid velocities significantly reduce the thickness of the film. 

Morsi SA, Alexander AJ (1972) An investigation of particle trajectories in two-phase flow systems. Journal of Fluid Mechanics 55 193-208... 

The single phase, two-component fluid system under consideration contains N molecules of which Nt are of species 1 and Nz are of species 2. The molecules of each species are labeled separately, so that the molecules of species a are numbered 1, 2,. . . Na. For simplicity, we suppose that each molecule contains three degrees of translational freedom and no other degrees of freedom. The positions of the molecules of species a are denoted by the sequence of three vectors R, , . . . , ... 

More than a century ago, Pickering [2] and Ramsden [3] investigated paraffin-water emulsions contains solid particles such as iron oxide, silicon dioxide, barium sulfate, and kaolin and discovered that these micron-sized colloids generate a resistant film at the interface between the two immiscible phases, inhibiting the coalescence of the emulsion drops. These so-called Pickering emulsions are formed by the self-assembly of colloidal particles at fluid-fluid interfaces in two-phase liquid systems (Fig. 1). 

In a similar way we can discuss the more complicated system a two-phase and two-constituent fluid system without memory which models (two-)phase equilibrium in fluid mixture. The model is composed of two phases (upper indices (2.105), (2.106)) each representing the (chemically) nonreacting fluid mixture containing two mutually nonreacting constituents (in the sense of Sect. 2.4 constituents are denoted by lower indices 1, 2). We have therefore two constituents distributed in two phases with the masses... 

Constitutive equations of this two-phase and two-constituent fluid system without memory are assumed in the form... 

Our steering results are demonstrated using an experimentally validated numerical model [20] of droplet motion inside the UCLA electrowetting system [21, 22], This model of EWOD fluid dynamics includes surface tensimi and electrowetting interface forces, viscous low Reynolds two-phase fluid flow, and the essential loss mechanisms due to contact angle saturatimi, triple point line pinning, and the related mechanism of contact angle hysteresis. 

Manipulating fluids in a two-phase flow system is much more complicated than in single-phase systems. Fluid flows can be actuated spontaneously, nonmechanically, or mechanically. The most frequently used flow actuation method, till now, is still pressure-driven pumps due to their availability and versatility. Especially, for a two-phase flow system, the naturally existing inhomogeneity makes other methods much more difficult to be applied. Electroosmosis, for instance, resulting from the force exerted on a space-charge region in the liquid by an electric field, will not work if the conductivity continuum in the fluid is interrupted by an entrapped dielectric liquid droplet or gas bubble. 

In a two-phase flow system, the different affinity of the two fluids for the wall makes (me fluid preferentially flow along comers due to the capillarity. As the number of the polygon sides decreases and the comers sharpen, the cross-sectional area of fluids held in comers increases, and comer flow becomes more important. Therefore, comer flow must be considered carefully in such processes as evaporation and drying of micro- and nanochannels with small angular polygonal cross sections. 

We have reviewed here the simplest, isothermal version of CDLG models for two-phase fluid dynamics on the microscopic scale. Applications of these models for studying interfacial dynamics in liquid-vapor and liquid-liquid systems in microcapillaries were discussed. The main advantage of our approach is that it models the exphcit dependence of the interfadal structure and dynamics on molecular interactions, including surfactant effects. However, an off-lattice model of microscopic MF dynamics may be required for incorporating viscoelastic and chain-connectivity effects in complex fluids. Isothermal CDLG MF dynamics is based on the same local conservation laws for species and momenta that serve as a foundation for mechanics, hydrodynamics and irreversible thermodynamics. As in hydrodynamics and irreversible thermodynamics, the isothermal version of CDLG model ean be... 

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