Transport binary systems

Mass Transport. An expression for the diffusive transport of the light component of a binary gas mixture in the radial direction in the gas centrifuge can be obtained directly from the general diffusion equation and an expression for the radial pressure gradient in the centrifuge. For diffusion in a binary system in the absence of temperature gradients and external forces, the general diffusion equation retains only the pressure diffusion and ordinary diffusion effects and takes the form... 

Transport of component i in a binary system is described by the equation of continuity [2], which is an expression for mass conservation of the subject component in the system, i.e.,... 

Polymer Transport in Binary Systems 2.1 Basic Theoretical Considerations... 

There are a number of quantitative features of Eq. (14) which are important in relation to rapid diffusional transport in binary systems. The mutual diffusion coefficient is primarily dependent on four parameters, namely the frictional coefficient 21 the virial coefficients, molecular weight of component 2 and its concentration. Therefore, for polymers for which water is a good solvent (strongly positive values of the virial coefficients), the magnitude of (D22)v and its concentration dependence will be a compromise between the increasing magnitude of with concentration and the increasing value of the virial expansion with concentration. 

In the following, we will often be concerned with ternary systems. Heterogeneous binary systems have two phases in equilibrium and are nonvariant (at given P and T). When two ternary phases are in contact, the system still has one (thermodynamic) degree of freedom. A ternary phase has three independent transport coefficients iee., Ln,L22, and /. ). 

After this formal discussion of chemical diffusion, let us now turn to some more practical aspects. In order to compare the formal theory with experiment, we have to carefully define the reference frame for the diffusion process, which is not trivial in the case of binary or multicomponent diffusion. To become acquainted with the philosophy of this problem, we deal briefly with defining a suitable reference frame in a binary system. Since only one (independent) transport coefficient is needed to describe chemical diffusion in a binary system, then according to Eqn. (4.57) we have in a one-dimensional system... 

We deal in this section with quasi-binary systems in which more than one product phase A, B forms between the reactants A(=AX) and B(=BX) (Fig. 6-9). The more interfaces separating the different product phases, the more likely it is that deviations from local equilibrium occur (the interfaces become polarized during transport as indicated in Fig. 6-9, curve b). Polarization of interfaces is the theme of Chapter 10. If, however, we assume that local equilibrium is established during reaction, the driving force of each individual phase (p) in the product is inversely... 

A distinction between solid/fluid and solid/solid boundaries is irrelevant from the point of view of transport theory. Solid/fluid boundaries in reacting systems are, for example, (A,B)/A, B, X (aq) or (A,B)/X2(g). More important is the distinction according to the number of components. In isothermal binary systems, the boundary is invariant if local equilibrium prevails. In higher than binary systems, the state of the a/fi interface is, in principle, variable and will be determined by the reaction kinetics, including the diffusion in the adjacent bulk phases. 

In practice, it is often feasible to reduce the multicomponent crystal in respect of its transport behavior to a quasi-binary system. Let us assume that the diffusion coefficients are DA>DB>DC, Dd, etc. The quasi-binary approach considers C, D, etc. as practically immobile, which means that A and B are interdiffusing in the im-... 

In a true binary system, the transport problem, which includes the boundary morphology, is completely defined by 1) the continuity equation (11.2) at the moving... 

Figure 11-6. Superposition of diffusive (/(diff)) and electrically driven (/(el)) transport in the (A,B)X/(B, A)X couple of the binary system AX-BX in analogy to Figure 11-3a. For Lf>Lf and sufficient driving force, the boundary b is morphologically unstable.

Figure 1 shows the results obtained by Francois and Skoulios (27) on the conductivity of various liquid crystalline phases in the binary systems water-sodium lauryl sulfate and water-potassium laurate at 50 °C. As might be expected, the water-continuous normal hexagonal phase has the highest conductivity among the liquid crystals while the lamellar phase with its bimolecular leaflets of surfactant has the lowest conductivity. Francois (28) has presented data on the conductivity of the hexagonal phases of other soaps. She has also discussed the mechanism of ion transport in the hexagonal phase and its similarity to ion transport in aqueous solutions of rodlike polyelectrolytes. 

FIGURE 14.5 Prediction of lidocaine transport number in the binary system (lidocaine-sodium) from the drug molar fraction in the anodal solution. The theoretical transport numbers were estimated using Equation 14.12 [59], and are compared with the experimental values from the literature [32]. A value of B = 1 was used for the prediction. 

Finally, it is worth reiterating that transport numbers are relatively complex functions of the concentration and mobility of all the ions present in the system. Thus, while the relationship between lidocaine molar fraction in the binary system (lidocaine-sodium) and the drug flux has been well defined [32,78], the results cannot be directly extrapolated to a different anodal composition. That is, the drug flux depends not only on its molar fraction [59], but also on the mobilities of the competing ions [115]. 

Subsequent to polymer manufacture, it is often necessary to remove dissolved volatiles, such as solvents, untreated monomer, moisture, and impurities from the product. Moreover, volatiles, water, and other components often need to be removed prior to the shaping step. For the dissolved volatiles to be removed, they must diffuse to some melt-vapor interface. This mass-transport operation, called devolatilization, constitutes an important elementary step in polymer processing, and is discussed in Chapter 8. For a detailed discussion of diffusion, the reader is referred to the many texts available on the subject here we will only present the equation of continuity for a binary system of constant density, where a low concentration of a minor component A diffuses through the major component ... 

Particle mixing is caused by the bubbles, partly be shear displacement or drift but also by the bulk transport of particles in the bubble wake. Bubbles may also cause segregation if there are different kinds of particles present. Unlike other kinds of mixers, segregation is insensitive to particle size difference but particularly sensitive to density difference. In a binary system of particles segregation increases approximately as particle density ratio to the power 5/2 but with particle size ratio only to the power 1/5 (11). This can cause problems in, for example, coal combustion where char has a markedly lower density than ash and also in some ore reduction processes using coke. 

We consider the hamiltonian (4.26) for a binary system (its extension to an arbitrary number of partners or to continuous disorder creates no difficulty in principle). The Schrodinger solution associated with this hamiltonian describes a coupling of very general occurrence, since it is encountered in conduction and transport phenomena, as well as in kinetics models of disordered systems ... 

The pyridine, being a highly volatile and mobile compound relative to n-dodecane, is able to escape the surface and be transported to it with great ease, thereby being depleted more rapidly than equilibrium. In contrast, the n-dodecane is retained. For the binary system under consideration there is a limit to this behavior, shown by the dashed line on Figure 7, which is the total evolution of pyridine with no evolution of n-dodecane. 

VT105 in that it is a richer command set and is a simple ASCII stream, it can be easily read with out resorting to decoding the bit patterns of characters. Graphics figures can be stored as simple sequential files, edited with a standard editor and transported between system (ours or other vendors) without worrying about the oddities of binary file structures and data being interpreted as control codes. ... 

One of the most interesting aspects of energy transport is the excitation percolation transition (, and its similarity (10) to magnetic phase transitions and other critical phenomena (, 8). In its simplest form the problem is one of connectivity. In a binary system, made only of hosts and donors, the question is can the excitation travel from one side of the material to the other The implicit assumption is that there are excitation-transfer-bonds only between two donors that are "close enough", where "close enough" has a practical aspect (e.g. defined by the excitation transfer probability or time). Obviously, if there is a succession of excitation-bonds from one edge of the material to the other, one has "percolation", i.e. a connected chain of donors forming an excitation conduit. We note that the excitation-bonds seldom correspond to real chemical bonds rather more often they correspond to van-der-Walls type bonds and most often they correspond to a dipole-dipole or equivalent quantum-mechanical interaction. 

Ultrasound in combination with an organic solvent facilitates the formation of binary systems with an aqueous electrolyte, thereby increasing the current intensity Figure 8.14B shows this effect on the sono-voltammogram of A/,A/,A/, /V -tetramethyl-p-phenylenediamine (TMPD) in 0.1 M aqueous KCI with and without the addition of 40% v/v heptane [156]. The increased current in the acoustically emulsified media was ascribed to enhanced transport of electroactive material in heptane droplets towards the electrode surface, and related to the analyte solubility in the organic phase. The ratio of the current increase to the volume fraction of organic solvent ([Pg.286]

The ZLC method offers advantages of speed and simplicity and requires only a very small adsorbent sample thus making it useful for characterization of new materials. The basic experiment using an inert carrier (usually He) measures the limiting transport difiiisivity (Do) at low concentration. A variant of the technique using isotopically labeled tracers (TZLC) yields the tracer diffiisivity and counter diffusion in a binary system may also be studied by this method. To obtain reliable results a number of preliminary experiments are needed, e.g. varying sample quality, nature of the purge gas, the flow rate and, if possible, particle size to confirm intracrystalline diffusion control. 

Olir discussion on diffusion will be restricted primarily to binary systems containing only species A and B. We now wish to determine how the molar diffusive flux of a species (i.e., Ja) is related to its concentration gradient. As an aid in the discussion of the transport law that is ordinarily used to describe diffusion, lesll similar laws ftom other trans K)it processes. For example, in conductive heat transfer the constitutive equation relating the heat flux q and the temperature gradient is Fourier s law ... 

This model includes the mumal coupling effect of the permeants. A positive or negative value of Ajj or Ajj indicates a positive or negative effect of the presence of one component on the transport of the other component. Sferrazza et al. [44] have analyzed the behavior of binary systems using an approach similar to that of Brun et al. [43]. They used a similar model to describe diffusion ... 

Considering the membrane process as a binary system, the transport of solvent (e.g., water), and solute are involved. Designating solute and solvent by subscripts A and B, Eq. (5) can be written for solvent B as... 

The analysis of turbulent eddy transport in binary systems given above is generalized here for multicomponent systems. The constitutive relation for j y in multicomponent mixtures taking account of the molecular diffusion and turbulent eddy contributions, is given by the matrix generalization of Eq. 10.3.1... 

---