Phase equilibrium surface tension

From the viscosity, as well as the phase equilibrium, surface tension, and density measurements it is evident that the system KF-K2M0O4-B2O3 is very complex. Beside the chemical reactions, the polymerization tendency of the melts, especially in the region of higher contents of boron oxide, makes this system difficult to study. 

The foregoing is an equilibrium analysis, yet some transient effects are probably important to film resilience. Rayleigh [182] noted that surface freshly formed by some insult to the film would have a greater than equilibrium surface tension (note Fig. 11-15). A recent analysis [222] of the effect of surface elasticity on foam stability relates the nonequilibrium surfactant surface coverage to the foam retention time or time for a bubble to pass through a wet foam. The adsorption process is important in a new means of obtaining a foam by supplying vapor phase surfactants [223]. 

A chemical s Tb, the temperature at which its vapor pressure equals the ambient pressure, and Tm, the temperature at which its solid and liquid forms are in equilibrium at ambient pressure, are easily located in references and databases. As a result, many of the correlations that have been constructed for property estimations use these parameters as independent variables. The Tb of a chemical can nonetheless provide an indication of the partitioning between gas and liquid phases,53 with the higher values denoting a lower tendency to exist in the vapor phase. The surface tension, y, of a chemical, the ratio of the work done to expand the surface divided by the increase in the surface area, is often used to estimate the VP of liquids in aerosols and in soil capillaries.28 The VP of a chemical is the pressure of a pure chemical vapor that is in equilibrium with the pure liquid or solid, and... 

This brings up the question of how this scheme has to be modified when equilibrium is not attained. The answer is that the identity of thermod3mamical and mechanical measurement persists, but that the value obtained for y differs from y (eq.) in fact, often y (non-eq.) > y (eq.). Suppose a given interface is created very rapidly and then starts to relax with a time scale r. At any time t equilibrium state, characterized by the pertaining y (non-eq.). Even then, this non-equilibrium surface tension can be measured, provided the time-scale of our measurement is short in comparison with t. When different methods of measurement, either thermodynamical or mechanical, do not yield the same y this may either mean that there have been errors in the measurement or that they apply to different moments (or time intervals) of the relaxation period. The downward tendency of y(f) reflects the general trend of F(V,T,n) and G(p,T, n) to become minimal at equilibrium (sec. 1.2.12). When only relaxation of the interface takes place, y must decrease. However, when the bulk phases also relax slowly or when the relaxation is determined by adsorption-desorption processes, y may also increase. For instance, this would be observed if... 

In recent years, several theoretical and experimental attempts have been performed to develop methods based on oscillations of supported drops or bubbles. For example, Tian et al. used quadrupole shape oscillations in order to estimate the equilibrium surface tension, Gibbs elasticity, and surface dilational viscosity [203]. Pratt and Thoraval [204] used a pulsed drop rheometer for measurements of the interfacial tension relaxation process of some oil soluble surfactants. The pulsed drop rheometer is based on an instantaneous expansion of a pendant water drop formed at the tip of a capillary in oil. After perturbation an interfacial relaxation sets in. The interfacial pressure decay is followed as a function of time. The oscillating bubble system uses oscillations of a bubble formed at the tip of a capillary. The amplitudes of the bubble area and pressure oscillations are measured to determine the dilational elasticity while the frequency dependence of the phase shift yields the exchange of matter mechanism at the bubble surface [205,206]. 

The foaminess 2 is an unequivocal function of the time tpc which is needed to obtain equilibrium surface tension, e.g. 2 = 1.85x10 x1.00 for BSA foams [5]. The area requirement of a single surface adsorbed molecule was obtained from do/dc, where c is the protein concentration, by the Gibbs relationship. By assuming the existence of a hydrate ion complex, which consists of protein and water molecules, the coordination numbers were estimated. By applying the phase change model from ref [6] for the adsorption and surface denaturation of BSA, a simple relationship was found between the dimensionless surface tension y and the time t ... 

A difuse interface model uses for description of a two-phase system an order parameter which changes continuously across the interphase boundary. This variable is often called a phase field , as its allows to define which of the alternative phases prevails at each location. We have already used this approach in Section 1.2 to compute equilibrium surface tension, and noticed that in a one-component fluid the only required order parameter is density. We shall now extend this model to non-equilibrium situations involving fluid flow. 

The surface tension is calculated starting from the parachor and the densities of the phases in equilibrium by the Sugden method (1924) J... 

A homogeneous metastable phase is always stable with respect to the fonnation of infinitesimal droplets, provided the surface tension a is positive. Between this extreme and the other thennodynamic equilibrium state, which is inhomogeneous and consists of two coexisting phases, a critical size droplet state exists, which is in unstable equilibrium. In the classical theory, one makes the capillarity approxunation the critical droplet is assumed homogeneous up to the boundary separating it from the metastable background and is assumed to be the same as the new phase in the bulk. Then the work of fonnation W R) of such a droplet of arbitrary radius R is the sum of the... 

Equilibration of the interface, and the establislnnent of equilibrium between the two phases, may be very slow. Holcomb et al [183] found that the density profile p(z) equilibrated much more quickly than tire profiles of nonnal and transverse pressure, f yy(z) and f jfz), respectively. The surface tension is proportional to the z-integral of Pj z)-Pj z). The bulk liquid in the slab may continue to contribute to this integral, indicatmg lack of equilibrium, for very long times if the initial liquid density is chosen a little too high or too low. A recent example of this kind of study, is the MD simulation of the liquid-vapour surface of water at temperatures between 316 and 573 K by Alejandre et al [184]. 

This database provides thermophysical property data (phase equilibrium data, critical data, transport properties, surface tensions, electrolyte data) for about 21 000 pure compounds and 101 000 mixtures. DETHERM, with its 4.2 million data sets, is produced by Dechema, FIZ Chcmic (Berlin, Germany) and DDBST GmhH (Oldenburg. Germany). Definitions of the more than SOO properties available in the database can be found in NUMERIGUIDE (sec Section 5.18). 

For many laboratoiy studies, a suitable reactor is a cell with independent agitation of each phase and an undisturbed interface of known area, like the item shown in Fig. 23-29d, Whether a rate process is controlled by a mass-transfer rate or a chemical reaction rate sometimes can be identified by simple parameters. When agitation is sufficient to produce a homogeneous dispersion and the rate varies with further increases of agitation, mass-transfer rates are likely to be significant. The effect of change in temperature is a major criterion-, a rise of 10°C (18°F) normally raises the rate of a chemical reaction by a factor of 2 to 3, but the mass-transfer rate by much less. There may be instances, however, where the combined effect on chemical equilibrium, diffusivity, viscosity, and surface tension also may give a comparable enhancement. 

First we look at the simpler case of the shrinking of a single cluster of radius R at two-phase coexistence. Assume that the phase inside this cluster and the surrounding phase are at thermodynamic equilibrium, apart from the surface tension associated with the cluster surface. This surface tension exerts a force or pressure inside the cluster, which makes the cluster energetically unfavorable so that it shrinks, under diffusive release of the conserved quantity (matter or energy) associated with the order parameter. 

In this table the parameters are defined as follows Bo is the boiling number, d i is the hydraulic diameter, / is the friction factor, h is the local heat transfer coefficient, k is the thermal conductivity, Nu is the Nusselt number, Pr is the Prandtl number, q is the heat flux, v is the specific volume, X is the Martinelli parameter, Xvt is the Martinelli parameter for laminar liquid-turbulent vapor flow, Xw is the Martinelli parameter for laminar liquid-laminar vapor flow, Xq is thermodynamic equilibrium quality, z is the streamwise coordinate, fi is the viscosity, p is the density, <7 is the surface tension the subscripts are L for saturated fluid, LG for property difference between saturated vapor and saturated liquid, G for saturated vapor, sp for singlephase, and tp for two-phase. 

The difference between the static or equilibrium and dynamic surface tension is often observed in the compression/expansion hysteresis present in most monolayer Yl/A isotherms (Fig. 8). In such cases, the compression isotherm is not coincident with the expansion one. For an insoluble monolayer, hysteresis may result from very rapid compression, collapse of the film to a surfactant bulk phase during compression, or compression of the film through a first or second order monolayer phase transition. In addition, any combination of these effects may be responsible for the observed hysteresis. Perhaps understandably, there has been no firm quantitative model for time-dependent relaxation effects in monolayers. However, if the basic monolayer properties such as ESP, stability limit, and composition are known, a qualitative description of the dynamic surface tension, or hysteresis, may be obtained. 

The purpose of this chapter is to introduce the effect of surfaces and interfaces on the thermodynamics of materials. While interface is a general term used for solid-solid, solid-liquid, liquid-liquid, solid-gas and liquid-gas boundaries, surface is the term normally used for the two latter types of phase boundary. The thermodynamic theory of interfaces between isotropic phases were first formulated by Gibbs [1], The treatment of such systems is based on the definition of an isotropic surface tension, cr, which is an excess surface stress per unit surface area. The Gibbs surface model for fluid surfaces is presented in Section 6.1 along with the derivation of the equilibrium conditions for curved interfaces, the Laplace equation. 

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