Diffusion multiphase systems

First a derivative is given of the equations of change for a pure fluid. Then the equations of change for a multicomponent fluid mixture are given (without proof), and a discussion is given of the range of applicability of these equations. Next the basic equations for a multicomponent mixture are specialized for binary mixtures, which are then discussed in considerably more detail. Finally diffusion processes in multicomponent systems, turbulent systems, multiphase systems, and systems with convection are discussed briefly. 

F.J.J. van Loo. Multiphase diffusion in binary and ternary solid-state systems // Prog.Solid St.Chem.- 1990.- V.20.- P.47-99. 

Problem Solving Methods Most, if not aU, problems or applications that involve mass transfer can be approached by a systematic-course of action. In the simplest cases, the unknown quantities are obvious. In more complex (e.g., iTmlticomponent, multiphase, multidimensional, nonisothermal, and/or transient) systems, it is more subtle to resolve the known and unknown quantities. For example, in multicomponent systems, one must know the fluxes of the components before predicting their effective diffusivities and vice versa. More will be said about that dilemma later. Once the known and unknown quantities are resolved, however, a combination of conservation equations, definitions, empirical relations, and properties are apphed to arrive at an answer. Figure 5-24 is a flowchart that illustrates the primary types of information and their relationships, and it apphes to many mass-transfer problems. 

For the analysis heat and mass transfer in concrete samples at high temperatures, the numerical model has been developed. It describes concrete, as a porous multiphase system which at local level is in thermodynamic balance with body interstice, filled by liquid water and gas phase. The model allows researching the dynamic characteristics of diffusion in view of concrete matrix phase transitions, which was usually described by means of experiments. 

Lithiated carbons are mostly multiphase systems. Hence, the determination of chemical diffusion coefficients for Li1 causes experimental problems because the propagation of a reaction front has to be considered. 

United States Patent 4,767,628 assigned to Imperial Chemical Industries describes a similar lactide/glycolide delivery system for LHRH polypeptide (122,123). A multiphase release pattern is again postulated. The first phase occurs by diffusion of drug through aqueous polypeptide domains linked to the exterior surface of the matrix. 

This method provides for one-dimensional diffusion and should be useful for studying mass transport to or from a variety of multiphase systems. The method provides for studying stirring rate dependence and the mass transport mechanisms related to the system under study. 

In this chapter, we consider multiphase (noncatalytic) systems in which substances in different phases react. This is a vast field, since the systems may involve two or three (or more) phases gas, liquid, and solid. We restrict our attention here to the case of two-phase systems to illustrate how the various types of possible rate processes (reaction, diffusion, and mass and heat transfer) are taken into account in a reaction model, although for the most part we treat isothermal situations. 

NAPL will migrate from the liquid phase into the vapor phase until the vapor pressure is reached for that liquid. NAPL will move from the liquid phase into the water phase until the solubility is reached. Also, NAPL will move from the gas phase into any water that is not saturated with respect to that NAPL. Because hydraulic conductivities can be so low under highly unsaturated conditions, the gas phase may move much more rapidly than either of the liquid phases, and NAPLs can be transported to wetter zones where the NAPL can then move from the gas phase to a previously uncontaminated water phase. To understand and model these multiphase systems, the characteristic behavior and the diffusion coefficients for each phase must be known for each sediment or type of porous media, leading to an incredible amount of information, much of which is at present lacking. 

J. J. Linderman, P. A. Mahama, K. E. Forsten, and D. A. Lauffenburger, Diffusion and Probability in Receptor Binding and Signaling Rakesh K. Jain, Transport Phenomena in Tumors R. Krishna, A Systems Approach to Multiphase Reactor Selection... 

Chen, H., Fang, Q., Yin, X.F., Fang, Z.L., A multiphase laminar flow diffusion chip with ion selective electrode detection. Micro Total Analysis Systems Proceedings pTAS 2002 symposium, 6th Nara, Japan, Nov. 3-7, 2002, 371-373. 

Figure 9.4c and 9.4d represent intermediate cases, 9.4c indicates partial miscibility we see a two-phase system of AB blends with different A/B ratios. This might be the result of segregation into the binodals. Figure 9.4d is called an interphase or a multiphase blend. The system is quasi-homogeneous, but it contains all A/B ratios between cpi = 0 and concentration gradients as a result of non-completed diffusion in a combination of well-compatible polymers. 

The thickness, x[f, of the ApBq layer is referred to as critical because the growth conditions for the layers of other compounds of a given multiphase system become indeed critical if x xj because all of them lose a source of the B atoms (actually, only substance B is such a source) and their growth at the expense of diffusion of the B atoms is stopped. This problem will be examined in more detail when analysing the process of simultaneous formation of two and multiple chemical compound layers. 

An unambiguous criterion to distinguish between the growth regimes of any compound layer is the availability or lack of diffusing atoms of a given kind for other layers of a multiphase binary system. Under conditions of reaction (chemical) control these atoms are still available, while under conditions of diffusion control already not, and this is all that is necessary to explain the absence of some part of compound layers from the A-B reaction couple. 

From a theoretical viewpoint, predicting the sequence of layer occurrence at the A-B interface would present no difficulties if the values of all the chemical constants entering a system of differential equations like (3.27) were known. For any multiphase binary system A-B, these values are determined by the physical-chemical properties of the elements A and B and their compounds. With their dependence on those properties established, the sequence of formation of compound layers would readily be predicted from the system of equations (3.27) or similar. Unfortunately, the theory of reaction diffusion has not yet reached this stage of its development. 

Clearly, if diffusion of one of the components (either A or B) prevails in all the compounds of a multiphase binary system, then only the layer of one of those compounds will grow. Probably, the previously mentioned Ti-Al system just belongs to such systems. Therefore, the results obtained by... 

The melting point of titanium is 1670°C, while that of aluminium is 660°C.142 In kelvins, these are 1943 K and 933 K, respectively. Thus, the temperature 625°C (898 K) amounts to 0.46 7melting of titanium and 0.96 melting of aluminium. Hence, at this temperature the aluminium atoms may be expected to be much more mobile in the crystal lattices of the titanium aluminides than the titanium atoms. This appears to be the case even with the Ti3Al intermetallic compound. The duplex structure of the Ti3Al layer in the Ti-TiAl diffusion couple (see Fig. 5.13 in Ref. 66) provides evidence that aluminium is the main diffusant. Otherwise, its microstructure would be homogeneous. This point will be explained in more detail in the next chapter devoted to the consideration of growth kinetics of the same compound layer in various reaction couples of a multiphase binary system. 

In some works including textbooks, it is proposed to compare the values of the thermodynamic functions calculated per certain amount of a diffusing element. In such a case, however, it would be necessary first to determine this element. Furthermore, in the compounds of a given multiphase system, enriched in component A, diffusion of the A atoms often prevails, whereas in those enriched in component B diffusion of the B atoms is dominant. This makes any comparison of such values of the thermodynamic functions quite meaningless. 

In the great majority of cases, a line of the markers located in the zinc phase displaces a few micrometres aside from a line located in the other phases, indicative of the crack formation at the interface with zinc. To understand the further course of the reaction-diffusion process after the rupture of any reaction couple, it is necessary first to analyse the growth kinetics of the same compound layer in different reaction couples of a multiphase binary system. This will be done in the next chapter. 

Under conditions of diffusion control, all other compound layers of a multiphase binary system, located between the two growing ones, are kinetically unstable. If these other layers were initially missing from the A-B couple, they will not occur in it until at least one of initial substances (either A or B) is completely exhausted. If present, they must disappear... 

During the time dt, the thickness of the ArBs layer increases by dyA3 at interface 3 as a result of diffusion of the A atoms from interface 2 to interface 3 and their subsequent partial chemical reaction (4.2) with the surface B atoms. In the ApBq-B reaction couple the ApBq phase acts as a source of diffusing A atoms. It must be clear, however, that the content of component A in this phase cannot be less than the lower limit of its homogeneity range. Hence, as reaction (4.2) proceeds, the ApBq compound becomes unstable and therefore should undergo a partial transformation into another compound of the A-B multiphase binary system. To reveal the essence of this transformation, let us consider one of the simplest cases, in... 

If diffusion of one of the components prevails in the growing layer of a chemical compound, then in the reaction couples consisting of one of other compounds of a multiphase system and the non-diffusing component or of... 

It appears relevant to note that many workers tend to overestimate the significance of thermodynamic predictions concerning the direction of the reaction-diffusion process. In fact, however, those only bear a likelihood character. Even if the free energy of formation of one compound from its constituents is -200 kJ mol-1, while that of the other is -20 kJ mol1, this does not necessarily mean, as often (tacitly or directly) assumed, that the former will occur first and the more so that its growth rate must be ten times greater than that of the latter. As exemplified with the growth rate of a compound layer in various diffusion couples of the same multiphase binary system, the opposite may well take place. 

W. Lengauer. Multiphase reaction diffusion in transition metal-carbon and transition metal-nitrogen systems // J.Alloys Compounds - 1995 - V.229 - P.80-92. 

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