Metastable vapor-liquid equilibrium

Figure 5. Sketches of several methodsusedtoputaliquidunda-mechanlcalteiision. (a) Acoustic method. A hemispherical piezoelectric transducer emits focused ultrasound bursts (arrows) into a bulk liquid [43]. (b) Metastable vapor-liquid equilibrium. A nanoporous membrane or gel mediates the equilibrium of a bulk volume of liquid and its subsaturated vapor [15]. (c) Bertbelot tube. A rigid container partially filled with a liquid in equilibrium with its vapor is heated until the liquid expands to fill the entire volume. Upon cooling, the liquid follows an isochore and its pressure decreases [44,45[. (d) Centrifugal method. A tube formed with two symmetrical bends at each end (a z-tube) is spun around its mid-point such that the pressure in the liquid drops due to the centripetal acceleration acting on the column of liquid [46[.

In Figure 8.12 the outer envelope is the locus of saturated equimolar liquid states and saturated equimolar vapor states. However, note that Figure 8.12 is not a phase-equilibrium diagram in Figure 8.12 every point on the two-phase line represents an equimolar mixture, but phases in vapor-liquid equilibrium generally do not have the same composition. Consequently, Figure 8.12 contains no tie lines across the two-phase region. Outside the saturation envelope, the mixtures are stable one-phase fluids. Underneath that envelope, the mixtures may be metastable one-phase fluids or they may be unstable to one phase (that is, they may exist as two-phases). 

A thermodynamic state is defined as a condition of a system characterized by properties of the system that can be reproduced. States can be at stable, unstable, or metastable equilibrium. The states can be in nonequilibrium as well. Equilibrium states are those where the macroscale changes are invariant with time. These will figure in the discussions on fugacity and vapor-liquid equilibrium. 

Figure 8.3. Equilibrium constants (log K) for the metastable coexistence of completely ordered and disordered CaMg(C03>2 with dolomite in its stable order/disorder state as a function of temperature at constant pressure. SAT refers to the vapor-liquid curve for pure H2O. (After Bowers et al., 1984.)...

Figure 8.10 Schematic Pv diagram for a pure substance with the solid phase included. Shaded regions are metastable and unstable states. Vapor-liquid critical point (filled square) occurs at the maximum in the vapor-pressure curve. Filled circles are the triple-point voliunes at which solid, liquid, and vapor all coexist in three-phase equilibrium.

However, for a rarefaction wave, the vapor becomes subcooled and the liquid becomes superheated. When the wave front passes, the liquid phase is assumed to adjust from the metastable state at an equilibrium rate. If isentropic processes are assumed, the mass transfer rate can be shown to be... 

Superheated liquids are liquids which exist at temperatures above their equilibrium boiling point at the system pressure. These liquids are metastable in a thermodynamic sense, i.e., they are stable with respect to small perturbations on the system, but if the perturbation is sufficiently large, superheated liquids will partially vaporize and form a final, more stable state, usually consisting of vapor and residual liquid. 

It is not obvious how AF varies with the size of a cluster, because vv depends on the size, but an indirect scheme is available for determining the desired information. For one particular size, R0, there is assumed to be a value of AF for a condition of stability. This means that for a superheated liquid at a stated temperature and pressure, one and only one cluster size is capable of existence for long. This cluster is called a nucleus. A stable cluster is really in a metastable state, as discussed later. However, for any degree of equilibrium, AF must be unaffected by infinitesimal changes in the cluster size. So d(AF)/dR = 0. If vv is defined as the volume occupied by one vapor molecule, then ny = 47r.fi o8/(3ty)- These two manipulations produce a solution for the quantity r v — vl in Eq. (40)... 

A vapor, when compressed to the point where its pressure exceeds its vapor pressure at that temperature, will condense to form liquid droplets, so that the final stable pressure is just the equilibrium vapor pressure. This condensation usually and readily takes place on dust particles, container walls, or ions formed by extraneous cosmic radiation or the like. Under extremely clean and ion-free conditions, however, it is possible to avoid condensation and achieve a metastable state in which the actual... 

Figure 7.5 Phase diagram of elemental sulfur, showing the stable solid phases a-sulfur (orthorhombic red sulfur ) and /3-sulfur (monoclinic yellow sulfur ) and equilibrium phase boundaries (solid lines) as well as the metastable phase boundary (dashed line) that connects a-sulfur to liquid and vapor phases.

When does a liquid boil Clearly, boiling at constant pressure—say, atmospheric pressure—begins when we increase the temperature of a liquid or solution and the vapor pressure reaches a pressure of one atmosphere. Alternatively, the pressure over a liquid or solution at constant temperature must be reduced until it reaches the vapor pressure at that temperature (e.g., vacuum distillation). Yet it is well known that liquids can be superheated (and vapors supersaturated) without the occurrence of phase transfer. In fact, liquids must always be superheated to some degree for nucleation to begin and for boiling to start. That is, the temperature must be raised above the value at which the equilibrium vapor pressure equals the surrounding pressure over the liquid, or the pressure must be reduced below the vapor pressure value. As defined earlier, these differences are called the degree of superheat. When the liquid is superheated, it is metastable and will reach equilibrium only when it breaks up into two phases. 

The vapor pressure at equilibrium depends on the temperature and the solution, but it is independent of the relative or absolute amounts of liquid and vapor. When air adjacent to pure water is saturated with water vapor (100% relative humidity), the gas phase has the maximum water vapor pressure possible at that temperature — unless it is supersaturated, a metastable, nonequilibrium situation. This saturation vapor pressure in equilibrium with pure water (P ) increases markedly with temperature (Fig. 2-16) for example, it increases from 0.61 kPa at 0°C to 2.34 kPa at 20°C to 7.38 kPa at 40°C (see Appendix I). Thus, heating air at constant pressure and constant water content causes the relative humidity to drop dramatically, where... 

From Vukalovich, Ivanov, Fokin, and Yakovlev, Thermophysical Properties of Mercury, Standartov, Moscow, 1971. For the saturated liquid the specific volume at 203.15 K is 7.26239 x 10 m Vkg, etc. All the tabular values for 203.15 K, 213.15 K, 223.15 K, and 233.15 K represent a metastable equilibrium between the subcooled liquid and the saturated vapor. 

If insuflicicnt condensation nuclei and/or surface arc available, condensation is delayed and the system passes into a metastable state, even though it is on the liquid side of the equilibrium curve. The ratio of the actual pressure of the vapor to the equilibrium vapor pressure at the temperature in question is the saluralion ratio (or relative Imuiidity) ... 

To start with, let us consider a particular case of metastable states - a liquid superheated with respect to the liquid-vapor equilibrium temperature. For simplicity let us take a pure liquid at positive pressures, see Fig. 1. The region of superheated states is limited from below by the binodal Ts(p) and from above by the experimental line of attainable superheat, or, in other words, the line of spontaneous boiling-up T (p Cxp) of the liquid. An understandable limitation is imposed on the volume of superheated sample V and the time period Cxp of experiment. Naturally, the experimental time should be shorter than the life time t of the metastable state. 

PRIMARY NUCLEATION. In scientific usage, nucleation refers to the birth of very small bodies of a new phase within a supersaturated homogenous existing phase. Basically, the phenomenon of nucleation is the same for crystallization from solution, crystallization from a melt, condensation of fog drops in a supercooled vapor, and generation of bubbles in a superheated liquid. In all instances, nucleation is a consequence of rapid local fluctuations on a molecular scale in a homogenous phase that is in a state of metastable equilibrium. The basic phenomenon is called homogeneous nucleation, which is further restricted to the formation of new particles within a phase iminfluenced in any way by solids of... 

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