Phase interface motion

Figure 11-17. a) Phase diagram of the quasi-binary system AX-BX with an extended miscibility gap. b) Schematic electrolysis cell A/AX/BX/B. Cation vacancy drift and the mechanism of interface motion are indicated. 

Periodic reactions of this kind have been mentioned before, for example, the Liese-gang type phenomena during internal oxidation. They take place in a solvent crystal by the interplay between transport in combination with supersaturation and nuclea-tion. The transport of two components, A and B, from different surfaces into the crystal eventually leads to the nucleation of a stable compound in the bulk after sufficient supersaturation. The collapse of this supersaturation subsequent to nucleation and the repeated build-up of a new supersaturation at the advancing reaction front is the characteristic feature of the Liesegang phenomenon. Its formal treatment is quite complicated, even under rather simplifying assumptions [C. Wagner (1950)]. Other non-monotonous reactions occur in driven systems, and some were mentioned in Section 10.4.2, where we discussed interface motion during phase transformations. 

A vast number of engineering materials are used in solid form, but during processing may be found in vapor or liquid phases. The vapor— solid (condensation) and liquid—>solid (solidification) transformations take place at a distinct interface whose motion determines the rate of formation of the solid. In this chapter we consider some of the factors that influence the kinetics of vapor/solid and liquid/solid interface motion. Because vapor and liquid phases lack long-range structural order, the primary structural features that may influence the motion of these interfaces are those at the solid surface. 

The conditions and kinetic equations for phase transformations are treated in Chapters 17 and 20 and involve local changes in free-energy density. The quantification of thermodynamic sources for kinetically active interface motion is approximate for at least two reasons. First, the system is out of equilibrium (the transformations are not reversible). Second, because differences in normal component of mechanical stresses (pressures, in the hydrostatic case) can exist and because the thermal con-... 

Solid/vapor interface motion can be produced by evaporation—the atoms that compose the solid phase are removed from the surface via the vapor phase reverse motion can be produced by condensation where a vapor-phase flux is directed onto the solid phase. Figure 14.2 illustrates how simultaneous evaporation and condensation can result in surface smoothing. 

The F( + )d methods, like techniques in the F(+)cd class, require differential flow for separation. However the nature of the differential flow differs in the two cases. Since the F(+)d methods induce enrichment only at an interface between two phases, the sole requirement of differential flow is that one phase assumes motion relative to another phase. It is usually an easy matter to instigate the relative motion of phases. 

The volume of fluid (VOF) approach simulates the motion of all the phases rather than tracking the motion of the interface itself. The motion of the interface is inferred indirectly through the motion of different phases separated by an interface. Motion of the different phases is tracked by solving an advection equation of a marker function or of a phase volume fraction. Thus, when a control volume is not entirely occupied by one phase, mixture properties are used while solving governing Eqs (4.1) and (4.2). This avoids abrupt changes in properties across a very thin interface. The properties appearing in Eqs (4.1) and (4.2) are related to the volume fraction of the th phase as follows ... 

Aqueous solutions containing anionic surfactants and alcohol cosurfactants were contacted with various oils. A microscope which utilized a vertical sample orientation and a video camera was used to observe and record the resulting diffusional processes. As a result, an improved and detailed viewing of intermediate phase growth, interface motion, and spontaneous emulsification was achieved. 

The aqueous solution at the highest salinity studied was entirely C in structure. No myelinic figures formed during the contacting experiment. The interface between C and brine remained smooth throughout. From Table IV, one can see that the interface motion was very much slower than that for lamellar aqueous structures. No contacting experiments were performed with solutions that were initially C+L because of problems with phase separation. 

The course of this process can be subdivided into several steps, in which a series of resistances have to be overcome. The fraction of these individual resistances in the total resistance can be very different. First, as a result of flow (convective transport) and molecular motion (diffusion transport), the vapour reaches the phase interface. In the next step the vapour condenses at the phase interface, and finally the enthalpy of condensation released at the interface is transported to the cooled wall by conduction and convection. Accordingly, three resistances in series have to be overcome the thermal resistance in the vapour phase, the thermal resistance during the conversion of the vapour into the liquid phase, and finally the resistance to heat transport in the liquid phase. 

For structuring, the IL has to be immobilised. This can be done using i.e. zeolitic structures or molecular sieves. It is obvious that with increasing surface area of the solid phase, the motion of the liquid and the proton transport will be hindered. From polymerisation experiments it is known that the stiffening of polymers by cross-linking can be compared with the polymer-surface interaction. Electrode surfaces and solids such as silica, carbon black or cathode powder also stiffen the polymer [52]. This can be explained by different transport properties at the interfaces. As a consequence it must be expected that at the surface of the added particles the ionic liquid will behave in a different way than in the immobilised liquid phase. 

This set of conditions is the one that is satisfied at large distances from the triple point in the Seppecher s phase field equations for the contact fine motion as in the phase field equations, our model assumes an unhindered interface motion, without caring for the heat transfer due to the latent heat. It also provides a theory consistent with the balance of normal stress across the fluid/fluid interface. The idea presented here opens the way to model fluid mechanical problems with contact line motion. This is something that is impossible with the Huh-Scriven solution without balancing the normal stress one... 

Fast motions of a bubble surface produce sound waves. Small (but non-zero) compressibility of the liquid is responsible for a finite velocity of acoustic signals propagation and leads to appearance of additional kind of the energy losses, called acoustic dissipation. When the bubble oscillates in a sound field, the acoustic losses entail an additional phase shift between the pressure in the incident wave and the interface motion. Since the bubbles are much more compressible than the surrounding liquid, the monopole sound scattering makes a major contribution to acoustic dissipation. The action of an incident wave on a bubble may be considered as spherically-symmetric for sound wavelengths in the liquid lr >Ro-When the spherical bubble with radius is at rest in the liquid at ambient pressure, pg), the internal pressure, p, differs from p by the value of capillary pressure, that is... 

As a consequence of these properties, partially relaxed NMR spectra can be used as a test for the assignment of the different resonances of polyethylene [86]. Results thus obtained have been analysed in terms of a three-phase model comprising lamellar crystallites, crystalline-amorphous interface and isotropic amorphous phase, and motions occurring in these different regions [86]. 

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