Two-phase boundary

The most popular theoretical description of the potentiometric behavior of ion-selective membranes makes use of the three-segmented membrane model introduced by Sollner53), Teorell 30,54), and Meyer and Sievers 31-5S). In this model the two phase boundaries and the interior of the membrane are treated separately. Here, the... 

The carbon removal reaction supposedly takes place at two-phase boundary of a solid catalyst, a solid reactantfcarbon particulate) and gaseous reactants(02, NO). Because of the experimental difficulty to supply a solid carbon continuously to reaction system, the reaction have been exclusively investigated by the temperature programmed reaction(TPR) technique in which the mixture of a catalyst and a soot is heated in gaseous reactants. 

Fig. 18 Phase space of PI-fc-PS-fc-PEO in vicinity of ODT. Filled and open circles-. ordered and disordered states, respectively, within experimental temperature range 100 < T/° C< 225. Outlined areas compositions with two- and three-domain lamellae (identified by sketches) shaded regions three network phases, core-shell double gyroid (Q230), orthorhombic (O70), and alternating gyroid (Q214). Overlap of latter two phase boundaries indicates high- and low-temperature occurrence, respectively, of each phase. Dashed line condition tfin = 0peo associated with symmetric PI-fc-PS-fc-PEO molecules. From [75]. Copyright 2004 American Chemical Society...

In this case the equations are greatly simplified and the ratio of the slopes of the two phase boundaries at xA =1 is given by the activity coefficients of B at infinite dilution in the liquid and solid phases [11] ... 

Figure 6.9 Two-dimensional projection of equilibrium at a plane of contact between three phases a, ft and % where the angles between the three two-phase boundaries meeting in a line of contact are denoted Qa, 9 and 9X.

A two-dimensional illustration of three phases a, ft and % in equilibrium is shown in Figure 6.9. Two phases coexist in equilibrium in planes perpendicular to the lines indicated in the two-dimensional figure and all three phases coexist along a common line also perpendicular to the plane of the drawing. Each of the three two-phase boundaries, which meet at the point of contact, has a characteristic interfacial tension, e.g. ca for the interface, which tends to reduce the area of the... 

For the NPEO vertical differentiation in the water column has also been demonstrated (see Fig. 6.4.1). The compounds showed a tendency to accumulate at the two-phase boundaries of air/fresh water and fresh water/saline water (the halocline), with concentration maxima observed at depths of 0 and 2 m [10], respectively. 

An interesting vertical profile of the metabolite concentrations was observed the compounds showed a tendency to accumulate at the two-phase boundaries of air-freshwater and freshwater-saline water (the halocline). Thus, concentration maxima were observed at depths of 0 and 2 m (see Fig. 6.4.1) [6]. The observed distribution may result from either the physicochemical properties of these compounds (surface activity and hydrophobicity), or their formation at the interface due to increased biological activity. For the parent surfactants a similar but less pronounced vertical distribution pattern was observed (with maxima at 0 and 2 m of 17 and 9 xg L 1, respectively) [5],... 

In each cell there are two phase boundaries giving rise to interphase potentials owing to unequal ionic distribution. The E.M.P. of such a cell is consequently given by the potential... 

The amount of oxygen adsorbed in the three-phase region has been found to depend linearly on the exchange current density for different catalyst-electrodes under similar conditions.31,32 This indicates that the electrocatalytic reaction takes place at the three-phase boundary. Vayenas and co-workers pointed out that for less porous electrodes the charge-transfer reaction at the two-phase boundary might become important and that under some conditions oxygen on the electrolyte surface itself might play a role. 

Nucleation and spinodal decomposition are poorly studied phenomena in gels. These processes accompany shear deformation around the two-phase boundaries even without external stresses, and the elastic energy is proportional to the volume of domains. As a result, the elastic effect becomes increasingly... 

In pigments that simulate natural pearl effects, the simplest case is a plateletshaped particle with two phase boundaries P, and P2 at the upper and lower surfaces of the particles, i.e., a single, thin, transparent layer of a material with a higher refractive index than its surroundings. For small flakes with a thickness of approx. 100 nm, the physical laws of thin, solid, optical films apply [5.203]. 

The salt bridge symbol represents the two phase boundaries on either side of the bridge. 

Figure 13.28. Vapor-liquid equilibria of some azeotropic and partially miscible liquids, (a) Effect of pressure on vapor-liquid equilibria of a typical homogeneous azeotropic mixture, acetone and water, (b) Uncommon behavior of the partially miscible system of methylethylketone and water whose two-phase boundary does not extend byond the y = x line, (c) x-y diagram of a partially miscible system represented by the Margules equation with the given parameters and vapor pressures Pj = 3, = 1 atm the broken line is not physically significant but is...

We propose signal processing of the UVP output. The gas-liquid interface is detected without using the echo intensity or any optical information. The method presented in this section represents an intermediate and necessary step in the development of an ultrasound-based sensor for reducing frictional drag. In the near future, a complete monitoring system for a bubbly two-phase boundary layer is to be developed. The system is to be applied to ships and pipelines. 

A stagnant film model is used for two-phase boundaries (1-2), which in effect, isolates the mass transfer process to a thin region at the interface stagnant film. Once the expressions for entropy production in terms of pressure, temperature, and composition are available a transformation is made to process variables such as reflux ratio, column height, packing or tray geometry, column diameter and column efficiency. Results of this design optimization model are compared with the results obtained via traditional methods. 

Hydrogen-Absorption Isotherms. The isotherms for the 25 weight % uranium alloy constitute a family of curves closely resembling each other. Seven of the 13 isotherms which were measured are plotted in Figure 3. Isotherms intermediate between each adjacent pair were omitted to reduce the complexity of the plot. The isotherms at 572° C. (not shown) and at 601° C. cross only two phase boundaries, because they are below the eutectic temperature. 

Calculate the compositions of the exiting raffinate and extract streams. Replot (or trace) Fig. 9.1 without the tie lines (Fig. 9.3). On Fig. 9.3, plot the mean-concentration point M. Now from mass-balance considerations, the exit concentrations must lie on the two phase-boundary lines and on a straight line passing through the mean concentration point. We know we want the water phase to have an exit concentration of 3 wt % alcohol. Such a concentration corresponds to point Ln on the graph. At point LN. the ether concentration is seen to be 7.6 wt % (this can be found more accurately in the present case by numerical extrapolation of the water-phase data in Table 9.1). Therefore, the composition of the raffinate stream is 3% alcohol, 7.6% ether, and (by difference) 89.4% water. 

Simplification (2) is questionable if it is assumed that the reactions at the two phase boundaries are rapid and that transport through the layer determines the rate of the overall process. This implies that at the two phase boundaries steady-state defect concentrations of different orders of magnitude will set in which will in turn produce a considerable concentration gradient at the surface layer between the phase boundaries. This is neglected in the theory by Cabrera and Mott. 

When Wq 0, a two-phase boundary layer with liquid flow must be considered, A number of analyses of problems of this type have been reported [22]-[28],... 

Aqueous film stability is dependent on the adhesive force or negative interfacial tension at the two-phase (i.e., solid/liquid) boundary. The force balance at the two-phase boundary may change independently from the three-phase force balance due to surface configuration change of interfacing surface state moieties, which occurs in order to minimize interfacial tension with water as described in previous chapters. 

Nonporous membrane techniques involve two or three phases separated by distinct phase boundaries. In three-phase membrane systems, a separate membrane phase is surrounded by two different liquid phases (donor and acceptor) forming a system with two phase-boundaries and thus two different extraction (partition) steps. These can be tailored to different types of chemical reactions, leading to a high degree of selectivity. The membrane phase can be a liquid, a polymer, or a gas, and the donor and acceptor phases can be either gas or hquid (aqueous or organic). Liquid membrane phases are often arranged in the pores of a porous hydrophobic membrane support material, which leads to a convenient experimental system, termed supported liquid membrane (SLM). There are several other ways to arrange a hquid membrane phase between two aqueous phases as described below. 

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