Phases interfaces between

There is, of course, a mass of rather direct evidence on orientation at the liquid-vapor interface, much of which is at least implicit in this chapter and in Chapter IV. The methods of statistical mechanics are applicable to the calculation of surface orientation of assymmetric molecules, usually by introducing an angular dependence to the inter-molecular potential function (see Refs. 67, 68, 77 as examples). Widom has applied a mean-held approximation to a lattice model to predict the tendency of AB molecules to adsorb and orient perpendicular to the interface between phases of AA and BB [78]. In the case of water, a molecular dynamics calculation concluded that the surface dipole density corresponded to a tendency for surface-OH groups to point toward the vapor phase [79]. 

Parallel flow. The direction of gas flow is parallel to the surface of the sohds phase. Contacting is primarily at the interface between phases, with possibly some penetration of gas into the voids among the solids near the surface. The solids bed is usually in a static-condition (Fig. 12-30). 

Our interest is in solution kinetics, so we will concern ourselves only with homogeneous reactions, which take place in a single phase. Heterogeneous reactions take place, at least in part, at interfaces between phases.) Further, we will mainly work with closed systems, those in which matter is neither gained nor lost during the period of observation. 

Chemists use a special notation to specify the structure of electrode compartments in a galvanic cell. The two electrodes in the Daniell cell, for instance, are denoted Zn(s) Zn2+(aq) and Cu2+(aq) Cu(s). Each vertical line represents an interface between phases—in this case, between solid metal and ions in solution in the order reactant product. 

FIGURE 2.1 Forces acting on charged particles near the interface between phases (a) and ((3). 

Despite the fact that Galvani potentials for individual interfaces between phases of different types cannot be determined, their existence and the physical reasons that they develop cannot be doubted. The combined values of Galvani potentials for certain sets of interfaces that can be measured or calculated are very important in electrochemistry (see Section 2.3.2). 

The final internal boundary condition applies to the interface between phase 1 and phase 2, and relates the flux of species Red] and Red2, at the ITIES, to the rate of the second-order redox reaction occurring at the interface. 

FIG. 9 Upper potential values, a.sds lower potential values, b.sds of the first oscillation at the interface between phases o and wl of the octanol membrane (A), interfacial potential of a two-phase octanol-water system in the absence of SDS, c.sds (B) and those in the presence of 10 mM SDS (in the case of inorganic electrolyte, 1 mM), d.sds (C)- TMACI tetramethylammonium chloride TEACI tetraethylammonium chloride TPACI tetrapropylammonium chloride TBACI tetra-butylammonium chloride AcNa sodium acetate PrNa sodium propionate, BuNa sodium n-butyrate VaNa sodium w-valerate. (Ref 27.)... 

FIG. 13 Apparatus for measuring electrical potential oscillation across the octanol membrane with application of current through the interface between phases o and wl (a) octanol phase, (b) aqueous phase, (c) Ag/AgCl reference electrode, (d) KCl salt bridge, and (e) saturated KCl. 

The CFD models considered up to this point are, as far as the momentum equation is concerned, designed for single-phase flows. In practice, many of the chemical reactors used in industry are truly multiphase, and must be described in the context of CFD by multiple momentum equations. There are, in fact, several levels of description that might be attempted. At the most detailed level, direct numerical simulation of the transport equations for all phases with fully resolved interfaces between phases is possible for only the simplest systems. For... 

Our discussion of multiphase CFD models has thus far focused on describing the mass and momentum balances for each phase. In applications to chemical reactors, we will frequently need to include chemical species and enthalpy balances. As mentioned previously, the multifluid models do not resolve the interfaces between phases and models based on correlations will be needed to close the interphase mass- and heat-transfer terms. To keep the notation simple, we will consider only a two-phase gas-solid system with ag + as = 1. If we denote the mass fractions of Nsp chemical species in each phase by Yga and Ysa, respectively, we can write the species balance equations as... 

As mentioned earlier, since the interfaces between phases are not resolved in the CFD model, the Reynolds-average mass-transfer terms and the... 

The term on the left side of the equation is the accumulation term, which accounts for the change in the total amount of species iheld in phase /c within a differential control volume. This term is assumed to be zero for all of the sandwich models discussed in this section because they are at steady state. The first term on the right side of the equation keeps track of the material that enters or leaves the control volume by mass transport. The remaining three terms account for material that is gained or lost due to chemical reactions. The first summation includes all electron-transfer reactions that occur at the interface between phase k and the electronically conducting phase (denoted as phase 1). The second summation accounts for all other interfacial reactions that do not include electron transfer, and the final term accounts for homogeneous reactions in phase k. 

In the above expression, ci k is the concentration of species i in phase k, and si kj is the stoichiometric coefficient of species i in phase k participating in heterogeneous reaction 1 (see eq 8). is the specific surface area (surface area per unit total volume) of the interface between phases k and p. ih.k- is the normal interfacial current transferred per unit interfacial area across the interface between the electronically conducting phase and phase k due to electron-transfer reaction h, and it is positive in the anodic direction. In the above expression, Faraday s law... 

Adhesion in which interfaces between phases or components are maintained by intermolecular forces, chain entanglements, or both, across the interfaces. 

As with catalytic reactions, our task is to develop pseudohomogeneous rate expressions to insert into the relevant mass-balance equations. For ary multiphase reactor where reaction occurs at the interface between phases, the reactions are pritnarily surface reactions (rate r ), and we have to find these expressions as functions of concentrations and rate and transport coefficients and then convert them into pseudohomogeneous expressions,... 

Interfacial electrochemistry is about electric charges at interfaces between phases, one of which is an electron conductor and the other an ion conductor. The kinetic part of the subject is about the rate at which these charges transfer across the interphase. However, this definition clearly embraces two limiting cases. 

The energy associated with the interfaces between phases plays an important part in certain aspects of the migration of petroleum in underground reservoirs. For this reason there has long been interest in the interfacial tension between the phases of petroleum. The work of Swartz (71) was one of the early efforts to determine the effect of changes in pressure and composition upon the interfacial tension between the liquid and gas phases of petroleum. The methods of determining the interfacial tension between phases have been improved and the pendant drop method (16, 25) appears to be one of the more useful approaches to such measurements, particularly at elevated pressures. 

Here, the reaction shown as Eq. 3-2 indicates the presence of an interface between phases 1 and 2. Unlike the case of absorption where attractions between 2 and 2 had to be broken and ones between 1 and 1 were made, now in this adsorption case die... 

In all our analyses of diffusion-limited layer growth, we have assumed that the interdiffusivities in the various phases were constants independent of concentration. In each case, the interfaces between phases were found to move parabolically with time. Suppose that assumption is relaxed and the interdiffusivities are allowed to vary with concentration. Will the interfaces still move parabolically ... 

An electrode is designated by representing the interfaces between phases by I. A cell diagram depicts the physical arrangement of species and interfaces, with any salt bridge denoted by II. 

Interfacial tension causes a pressure difference to exist across a curved surface, the pressure being greater on the concave side (i.e., on the inside of a droplet or bubble). Consider an interface between phase A, in a droplet or bubble, and phase B, surrounding the droplet or bubble. These will have pressures pA and pB. If the principal radii of curvature are Rx and R2 then,... 

The relationship between the five peroxide mechanism reaction steps can be seen in the reaction mechanism graph in Figure 4. As defined above, each step occurs at one of the five nodes, and the directed edges give the forward direction for the mechanism. Current-carriers for the overall mechanism are in boxes, while carbonate ions that continue from one cycle to the next are circled. Dashed vertical lines represent interfaces between phases. Nodes on the gas-electrolyte interface represent reaction steps occurring at that interface nodes attached to the electrolyte-solid interface represent reaction steps occurring at sites on the surface of the solid phase. The location of each reaction on this reaction mechanism graph follows the description of the... 

It seems also relevant to emphasise that in the absense of stress the position of the ApBq layer as a whole relative to the initial interface between phases A and B (see Fig. 1.8) only depends on the stoichiometry of the ApBq chemical compound but by no means on the faster diffusing species in the crystal lattice of this compound. The initial interface cannot therefore serve... 

The Kirkendall effect arises from the different values of the self-diffusion coefficients of the components of a substitutional solid solution, determined by Matano s method. Matano s interface is defined by the condition that as much of the diffusing atoms have migrated away from the one side as have entered the other. If DA = DB, its position coincides with the initial interface between phases A and B. If I)A f DB, it displaces into the side of a faster diffusant (see Fig. 1.22c). Note that KirkendalFs discovery only relates to disordered phases. It was indeed a discovery since at that time most reseachers considered the relation l)A = DB to hold for any solid solution of substitutional type. KirkendalFs experiments showed that in fact this is not always the case. 

Different diffusional contributions of the components of a chemical compound to the growth process of its layer at the interface between phases A and B should not be regarded as a manifestation or result of the Kirkendall effect since the fact that these contributions are in general different became known far before discovering this effect, the essence of which consists in different diffusivities of the components of a substitutional solid solution. 

A. Vapor pressure lowering, boiling point elevation, and freezing point lowering may all be visualized as a result of solute particles interfering with the interface between phases in a consistent way. This is not the case for viscosity. 

Catalysis can be classified as homogeneous catalysis, in which only one phase is involved, and heterogeneous catalysis, the case of interest here, in which the reaction occurs at or near an interface between phases [1],... 

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