Between phases, definition

Note that a. B may reflect either kinetic or equilibrium isotope partitioning between phases A and B. As discussed in the previous chapter, a -B for Fe/ Fe ratios typically varies between 0.997 and 1.003 (Chapter lOA Beard and Johnson 2004). In general, we will describe isotopic fractionations using A. b, following standard definitions ... 

Figure 10 is a ternary diagram for the systems Triolein/S/ Methanol, where S is respectively 4/1 molar ratios of 2-octanol to bis(2-ethylhexyl) sodium sulfosuccinate, triethylammonium linoleate or tetradecyldimethyl ammonium linoleate at 25°C. Not much difference is noted between phase areas for the triethylammonium linoleate and bis(2-ethylhexyl) sodium sulfosuccinate systems. Both are definitely inferior to the tetradecyldimethylammonium linoleate which shows the greatest solubilized area of methanol in triolein at 25°C. 

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. 

Transport phenomena can take place between phases, as well as within one phase. Let us begin with the simpler case of transport phenomena within one phase, in connection with the definitions of transport properties. 

In the definition of c, one must generally assume that any chemical component is free to penetrate into any phase, even if the partitioning between phases varies strongly from component to component. Hence, c is the number of independent chemical components found in any phase, to account for the limiting case in which different chemical components partition completely (within limits of experimental detection) into different phases. 

As the gas flow rate increases beyond that at minimum fluidization, the bed may continue to expand and remain homogeneous for a time. At a fairly definite velocity, however, bubbles begin to form. Further increases in flow rate distribute themselves between the dense and bubble phases in some ways that are not well correlated. Extensive bubbling is undesirable when intimate contading between phases is desired, as in drying processes or solid catalytic reactions. In order to permit bubble formation, the... 

By definition, the transmissive boundary between phases a and /3 allows the passage of a -+faradaic current owing to the interfacial transfer of the corresponding... 

In these discussions we will thus use the following explicit definition of a chemical measurement in the atmosphere the collection of a definable atmospheric phase as well as the determination of a specific chemical moiety with definable precision and accuracy. This definition is required since most atmospheric pollutants are not inert gaseous and aerosol species with atmospheric concentrations determined by source strength and physical dispersion processes alone. Instead they may undergo gas-phase, liquid-phase, or surface-mediated conversions (some reversible) and, in certain cases, mass transfer between phases may be kinetically limited. Analytical methods for chemical species in the atmosphere must transcend these complications from chemical transformations and microphysical processes in order to be useful adjuncts to atmospheric chemistry studies. 

What we mean in this report by equilibrium and disequilibrium requires a brief discussion of definitions. Natural physicochemical systems contain gases, liquids and solids with interfaces forming the boundary between phases and with some solubility of the components from one phase in another depending on the chemical potential of each component. When equilibrium is reached by a heterogeneous system, the rate of transfer of any component between phases is equal in both directions across every interface. This definition demands that all solution reactions in the liquid phase be simultaneously in equilibrium with both gas and solid phases which make contact with that liquid. Homogeneous solution phase reactions, however, are commonly much faster than gas phase or solid phase reactions and faster than gas-liquid, gas-solid and... 

Thus far, the discussion of reaction rate has been confined to homogeneous reactions taking place in a closed system of uniform composition, temperature, and pressure. However, many reactions are heterogeneous they occur at the interface between phases, for example, the interface between two fluid phases (gas-liquid, liquid-liquid), the interface between a fluid and solid phase, and the interface between two solid phases. In order to obtain a convenient, specific rate of reaction it is necessary to normalize the reaction rate by the interfacial surface area available for the reaction. The interfacial area must be of uniform composition, temperature, and pressure. Frequently, the interfacial area is not known and alternative definitions of the specific rate are useful. Some examples of these types of rates are ... 

Other important definitions include those of homogeneous, heterogeneous, and irreversible reactions. A homogeneous reaction occurs within a single phase, as in a stream that is, + HCOj = H2CO3. Heterogeneous reactions occur between phases, as gas-water, water-mineral, or, rarely, gas-mineral, as illustrated by the following reactions... 

Inclusion of this technique to the BOHLM has to be explained. Solvent extraction or partition of the solute between two immiscible phases is an equilibrium-based separation process. So, the membrane-based or nondispersive solvent extraction process has to be equilibrium based also. Liquid membrane separation is a rate process and the separation occurs due to a chemical potential gradient, not by equilibrium between phases [114]. According to these definitions, many authors who refer to their works as membrane-based or nondispersive solvent extraction processes are not correct. 

In laminar flow, /f reduces to a delta function. In turbulent flow, /f can be modeled using PDF methods. Thus, by definition, there is no mass transfer between phases. 

By definition, oTp -i- off = 1 and, in the absence of mass transfer between phases, the right-hand side of Eq. (4.50) is null. In this limit, Eq. (4.56) should reduce to... 

As defined in Appendix 5 compatibilization means A process of modification of interfacial properties of an immiscible polymer blend, leading to creation of polymer alloy . A polymer alloy in turn is defined as An immiscible polymer blend having a modified interface and/or morphology , whereas a polymer blend is simply A mixture of at least two polymers or copolymers . In other words, all polymer alloys are blends, but not all polymer blends are alloys. A somewhat more elaborate definition of a polymer alloy would describe a blend of at least two immiscible polymers stabilized either by covalent bond or ionic bond formation between phases, or by attractive intermolecular interaction, e.g., dipole-dipole, ion-dipole, charge-transfer, H-bonding, van der Waals forces, etc. 

During the experiments conducted up to this point, it was, therefore, not possible to give the solid bulk phase definite forms. Still, it could be shown by the experiments illustrated in Fig. 5 that the rate of reaction depended on the size of the solid phase which was here varied between 0.1 and 2.0 g. 

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