Phase boundary liquid-vapour

A phase is a part of a system that is chemically uniform and has a boundary around it. Phases can be solids, liquids and gases, and, on passing from one phase to another, it is necessary to cross a phase boundary. Liquid water, water vapour and ice are the three phases found in the water system. In a mixture of water and ice it is necessary to pass a boundary on going from one phase, say ice, to the other, water. 

As the temperature of the liquid phase is increased, the system ultimately reaches a phase boundary, the bubble point at which the gas phase (vapour) begins to appear, with the composition shown at the left end of the horizontal two-phase tie-line . As the temperature rises more gas appears and the relative amounts of the two phases are detemiined by applying a lever-ami principle to the tie-line the ratio of the fractionof molecules in the gas phase to that hn the liquid phase is given by the inverse of the ratio of the distances from the phase boundary to the position of the overall mole fraction Xq of the system. 

Surface waves at an interface between two innniscible fluids involve effects due to gravity (g) and surface tension (a) forces. (In this section, o denotes surface tension and a denotes the stress tensor. The two should not be coiifiised with one another.) In a hydrodynamic approach, the interface is treated as a sharp boundary and the two bulk phases as incompressible. The Navier-Stokes equations for the two bulk phases (balance of macroscopic forces is the mgredient) along with the boundary condition at the interface (surface tension o enters here) are solved for possible hamionic oscillations of the interface of the fomi, exp [-(iu + s)t + i V-.r], where m is the frequency, is the damping coefficient, s tlie 2-d wavevector of the periodic oscillation and. ra 2-d vector parallel to the surface. For a liquid-vapour interface which we consider, away from the critical point, the vapour density is negligible compared to the liquid density and one obtains the hydrodynamic dispersion relation for surface waves + s>tf. The temi gq in the dispersion relation arises from... 

Similar results, to the Fe-Zn system were obtained in the Ti,j,-Al(,) and Ti(j)-Al, ) system where, in the solid-liquid couples some of the expected surface layer phases were not formed, whereas in the solid-vapour system it was possible to obtain all the phases and predict from the AG -concen-tration curves the compositions at the different layer phase boundaries. 

The theoretical treatment which has been developed in Sections 10.2-10.4 relates to mass transfer within a single phase in which no discontinuities exist. In many important applications of mass transfer, however, material is transferred across a phase boundary. Thus, in distillation a vapour and liquid are brought into contact in the fractionating column and the more volatile material is transferred from the liquid to the vapour while the less volatile constituent is transferred in the opposite direction this is an example of equimolecular counterdiffusion. In gas absorption, the soluble gas diffuses to the surface, dissolves in the liquid, and then passes into the bulk of the liquid, and the carrier gas is not transferred. In both of these examples, one phase is a liquid and the other a gas. In liquid -liquid extraction however, a solute is transferred from one liquid solvent to another across a phase boundary, and in the dissolution of a crystal the solute is transferred from a solid to a liquid. 

An alternative explanation concerns the existence of two equilibria. As the vapour/liquid equilibrium is disturbed by the passage of air, the concentration of dissolved compounds in the liquid phase falls, disturbing the solid /liquid equilibrium. The kinetics of transfer across this latter phase boundary are much slower than for the liquid/vapour transfer, so that the extraction of odour becomes limited by the rate of diffusion into the liquid phase. 

Transports of HTO vapour and H20 vapour to and from surfaces are controlled similarly by eddy diffusion in the free air and molecular diffusion across the viscous boundary layer near the surface. There is also a liquid phase boundary layer, and diffusion through this is a limiting resistance to the transport of sparingly soluble gases such as H2 or HT. For HTO, the liquid film resistance is negligible (Slinn et al., 1978). When the concentration gradients are in opposite directions, transport of HTO to a water surface can proceed simultaneously with evaporation of H20. 

Using this equation AHV can be estimated with a knowledge of the equilibrium vapour pressure of a liquid at two different temperatures. For the solid-vapour phase boundary (sublimation), an analogous equation is obtained by replacing AHv with the heat of sublimation AHs. 

Another option is to derive equations for the pressures at which condensation takes place in narrow capillaries. Let us illustrate this for slits. As before, the characteristic function -kTlnS of the grand canonical partition function equals -pV + y A, with V = Ah. Let liquid and vapour coexist Inside the capillary and assume that we have only these two phases (i.e. the contribution of the (thin) inhomogeneity at the phase boundary to is Ignored). Equilibrium... 

Equimolar counter diffusion appears in the distillation of binary mixtures. In a distillation column the liquid falls downwards, and the vapour flows upwards, Fig. 1.43. As the liquid flowing down the column is colder than the vapour flowing upwards, chiefly the component with the higher boiling point, the so called least volatile component condenses, whilst the vapour from the boiling liquid mainly consists of the components with the lower boiling points, the more volatile components. The molar enthalpy of vaporization is, according to Trouton s rule, approximately constant for all components. If a certain amount of the least volatile component condenses out from the vapour, then the same number of moles of the more volatile substance will be evaporated out of the liquid. At the phase boundary between liquid and vapour we have cAwA = —cBwB. The reference velocity u is zero because cu = cAwA + cBwB. The molar flux transported to the phase boundary from (1.158) and (1.160) is... 

The region of saturated boiling is followed by that of convective evaporation. With the increasing vapour content the heat transfer from the wall to the fluid improves. The thermal resistance of the boundary layer decreases in comparison to the thermal resistances in nucleate boiling. Likewise, the wall temperature drops, cf. Fig. 4.53, so that only a few or no bubbles are formed at the wall. The heat transfer is predominantly or exclusively determined by evaporation at the phase boundary between the liquid at the wall and the vapour in the core flow. 

If vacuum is applied, the phase boundary between liquid and vapour is reached at a certain pressure and water starts to vaporize. To prevent a loss of temperature, heat -the so-called heat of evaporation - has to be introduced from the outside. If all water has been evaporated, a rise in temperature will ensue that can be taken as an indicator for the end of the drying process. Although this method is gentle, the material to be dried is puffed up and structural and cell deformations follow. 

Before describing surfactant adsorption at A/L and L/L interfaces, it is essential first to define the interface. The surface of a liquid is the boundary between two bulk phases, namely liquid and air (or the liquid vapour). Similarly, an interface between two immiscible liquids (oil and water) may be defined, provided that a dividing line is introduced as the interfacial region is not a layer of one-molecule thickness rather, it usually has a thickness 8 with properties that are different from the two bulk phases a and p [1]. However, Gibbs [2] introduced the concept of a mathematical dividing plane in the interfacial region (Figure 5.1)... 

Bivariant Systems.—If we examine Figs. 3 and 4, we see that the curves OA, OB, OC, which represent diagrammatically the conditions under which the systems, solid and vapour, liquid and vapour, solid and liquid, are in equilibrium, form the boundaries of three fields or areas. These areas give the conditions of temperature and pressure under which the single phases, solid, liquid and vapour, are capable of stable existence. These different areas are the regions of stability of the phase common to the two curves by which the area is enclosed. Thus, the phase common to the two systems represented by OA (solid and vapour) and OB (liquid and vapour) is the vapour phase and the area enclosed by the curves AO and OB is therefore the area of the vapour phase. Similarly, the area AOC is the area of the solid phase, and BOC the area of the liquid phase. 

Fig. 1. Liquid-vapour phase boundary in the temperature-entropy diagram for a substance of low and high specific heat. Water cV=3.5, PPl (C6F14) Cv=39.3.

The outer boundary of liquid water (of any liquid phase in general), which is in contact with its vapour or the air, is called the surface. The surface forming a boundary between two or more separate phases (phase boundary), such as liquid-gas, liquid-solid, gas-solid, or, for immiscible materials, Hquid-liquid or solid-solid, is called the interface. The surface or interface can be planar or curved. Thermodynamic properties of systems with planar and curved phase interfaces are different. 

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