Near-Critical Interface

In three dimensions, 9 = 2v l.26 and Ra = (To Q flk Tc=0. i9. Not only are the scaling relations (7.67) and (7.68) obtained from the simplified model in agreement with RG theory, the estimated value of the amplitude ratio R 0.39 is close to the universal theoretical value 7 o = 0-37. This value is confirmed by the most reliable experiments on fluids. Relationships between other thermodynamic properties and the diverging correlation length can be obtained in a similar fashion. 

Near-critical fluctuations modify not only the temperature dependence of the surface tension but also the shape of the density/concentration profile. RG theory shows that the universal expression for the order-parameter profile near the critical point can be written in terms of a universal scaling function,  

---

Much of what has been done on the theory of the near-critical interface has been within the framework of the van der Waals theory of Chapter 3, so much of our present understanding of the properties of those interfaces comes from that theory or from some suitably modified or extended version of it. As we shall see, an interface thickens as Hs critical point is approached, and the gradients of denaty and composition in the interface are then small. Thus, the view that the interfadal region may be treated as matter in bulk, with a local free-energy density that is that of a hypothetically uniform fluid of composition equal to the local composition, with an additional term arising from the non-uniformity, and that the latter may be approximated by a gradient expansion, typically truncated in second order, is then most likely to be successful and perhaps even quantitatively accurate. In this section we shall see what the simplest theory of that kind— that which comes from treating simple models in mean-field approximation, as in Chapter 5— yields for the structure and tension of an interface near a critical point. 

We turn next to the question of how to modify the mean-field theory of the near-critical interface that was outlined in 8 9.1, so as to incorporate in it the correct, non-classical values of the critical-point exponents. 

Based on the above results and discussion, the mechanism for the rhythmic oscillations at the oil/water interface with surfactant and alcohol molecules may be explained in the following way [3,47,48] with reference to Table 1. As the first step, surfactant and alcohol molecules diffuse from the bulk aqueous phase to the interface. The surfactant and alcohol molecules near the interface tend to form a monolayer. When the concentration of the surfactant together with the alcohol reaches an upper critical value, the surfactant molecules are abruptly transferred to the organic phase with the formation of inverted micelles or inverted microemulsions. This step should be associated with the transfer of alcohol from the interface to the organic phase. Thus, when the concentration of the surfactant at the interface decreases below the lower critical value, accumulation of the surfactant begins and the cycle is repeated. Rhythmic changes in the electrical potential and the interface tension are thus generated. 

A) The composition profile near the liquid-solid interface for steady-state freezing. (B) The temperature in the liquid near the interface, Tj, and the equilibrium liq-uidus temperature, Te, corresponding to the local composition. The region where Tl < Te is supercooled so dendrites can form. Dendrites cannot form if the actual thermal gradient is greater than the critical gradient. 

Eventually, the velocity of vapor in the jets becomes so large that the jets themselves become unstable near the interface as a result of Helmholtz instability (of wavelength XH) as shown in Fig. 15.63). The breakup of the jets destroys the efficient vapor-removal mechanism, increases vapor accumulation at the interface, and leads to liquid starvation at the surface and to the critical heat flux phenomenon. If jet breakup occurs at a vapor velocity UH within the jets, the critical heat flux q"m is given by... 

Several important criteria must be satisfied to stabilize a colloid in an SCF [5,6,8,9]. The surfactant must adsorb at the interface, and the surfactant tails must be solvated and long enough to provide steric stabilization, where the force between the droplets or particles is repulsive. Near-critical propane can solvate the tails of many hydrocarbon-based surfactants which are also utilized to form microemulsions in alkanes such as hexane, for example, bis-2-... 

This focus on phase behavior brought about the understanding that some of the reactions that had been successfully accomplished in supercritical carbon dioxide were actually taking place in the liquid phase (or at the interface) of a heterogeneous liquid-vapor system. Similarly, reactions carried out in liquid, near-critical propane had shown that this solvent displayed the same advantages as those of truly supercritical ones. The fact is that the densities of liquid mixtures close to the mixture s critical line are sufficiently lower than those of a classical Hquid to exhibit the same type of property values (lower viscosity, higher diffusivity, higher so-... 

Optohydrodynamics Fluid Actuation by Light, Fig. 2 Variation of the interface bending for increasing beam power P (a) upward and (b) downward continuous Ar" laser beam (wavelength in vacuum io = 514 nm) of beam waist coo- The theoretical profiles (solid lines) are calculated from Eq. 7. Experiments are performed in a phase-separated near-critical binary liquid mixture in order to drastically reduce the interfacial tension when approaching in temperature the critical temperature Tc-... 

These considerations apply to the tension between an oil-continuous and a water-continuous phase. The interface is covered by a surfactant monolayer and hence is relatively thin. However, attraction between micelles or droplets can canse separation into, for example, two water-continuous phases, one having a higher concentration of aggregates than the other. In this case the interface can be mueh thicker (e.g., on the order of a few droplet diameters) and interfacial tension can be low. In the limiting case of near criticality between the phases, the tension approaches zero and interfacial thickness becomes very large. 

This equation shows that k has the dimension ofm s . Moreover, k must be a constant as long as C is not too high. Above some critical concentration eq 3.1 can be expected not too hold any longer because of nonlinearities due to interactions between solute partieles S at, or near, the interface. 

---