Multiphase diffusion

In connection with multiphase diffusion another poorly understood topic should be mentioned—namely, the diffusion through porous media. This topic is of importance in connection with the drying of solids, the diffusion in catalyst pellets, and the recovery of petroleum. It is quite common to use Fick s laws to describe diffusion through porous media fJ14). However, the mass transfer is possibly taking place partly by gaseous diffusion and partially by liquid-phase diffusion along the surface of the capillary tubes if the pores are sufficiently small, Knudsen gas flow may prevail (W7, Bl). 

Table 4.2 Activation energies for nonmetal diffusion in various carbide and nitride phases of Group 4 and 5 determined by multiphase diffusion couples. Estimated error 0.05 eV ( 4.8 kJ/mol)...

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. 

Direct measurement of particle velocity and velocity fluctuations in fluidized beds or riser reactors is necessary for validating multiphase models. Dudukovic [14] and Roy and Dudukovic [28] have used computer-automated radioactive particle tracking (CARPT) to foUow particles in a riser reactor. From their measurements, it was possible to calculate axial and radial solids diffusion as well as the granular temperature from a multiphase KTGF model. Figure 15.10 shows one such measurement... 

In PEMFCs, the membrane electrode assembly (MEA, Eig. 15.2a) is a multilayer sandwich composed of catalytic layers (CLs) where electrochemical reactions take place, gas-diffusion media providing access of gases to the CLs, and a proton exchange membrane (PEM) such as Nafion . The CL is a multiphase multicomponent medium comprising ... 

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. 

Liquid-liquid multiphasic catalysis with the catalyst present in the ionic liquid phase relies on the transfer of organic substrates into the ionic liquid or reactions must occur at the phase boundary. One important parameter for the development of kinetic models (which are crucial for up-scaling and proper economic evaluation) is the location of the reaction. Does the reaction take place in the bulk of the liquid, in the diffusion layer or immediately at the surface of the ionic liquid droplets ... 

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. 

This chapter starts with a short introduction on the skin barrier s properties and the methods employed for analyzing experimental data. This is followed by an overview of several selected approaches to predict steady-state diffusion through the skin. Then a few approaches that approximate the structural complexity of the skin by predicting drug diffusion in biphasic or even multiphasic two-dimensional models will be presented. Finally, the chapter concludes with a short summary of the many variables possibly influencing drug permeation and penetration. 

Wang TF, Kasting GB, Nitsche JM (2006) A multiphase microscopic diffusion model for stratum comeum permeability. 1. Formulation, solution, and illustrative results for representative compounds. J Pharm Sci 95 620-647. 

E. C. Kumbur, K. V. Sharp, and M. M. Mench. Validated Leverett approach for multiphase flow in PEFC diffusion media. I. Hydrophobicity effect. Journal of the Electrochemical Society 154 (2007) B1295-B1304. 

Reactions carried in aqueous multiphase catalysis are accompanied by mass transport steps at the L/L- as well as at the G/L-interface followed by chemical reaction, presumably within the bulk of the catalyst phase. Therefore an evaluation of mass transport rates in relation to the reaction rate is an essential task in order to gain a realistic mathematic expression for the overall reaction rate. Since the volume hold-ups of the liquid phases are the same and water exhibits a higher surface tension, it is obvious that the organic and gas phases are dispersed in the aqueous phase. In terms of the film model there are laminar boundary layers on both sides of an interphase where transport of the substrates takes place due to concentration gradients by diffusion. The overall transport coefficient /cl can then be calculated based on the resistances on both sides of the interphase (Eq. 1) ... 

---