Diffusion cell method

Several experimental techniques have been developed for the investigation of the mass transport in porous catalysts. Most of them have been employed to determine the effective diffusivities in binary gas mixtures and at isothermal conditions. In some investigations, the experimental data are treated with the more refined dusty gas model (DGM) and its modifications. The diffusion cell and gas chromatographic methods are the most widely used when investigating mass transport in porous catalysts and for the measurement of the effective diffusivities. These methods, with examples of their application in simple situations, are briefly outlined in the following discussion. A review on the methods for experimental evaluation of the effective diffusivity by Haynes [1] and a comprehensive description of the diffusion cell method by Park and Do [2] contain many useful details and additional information. 

A typical experimental arrangement used for diffusion measurements consists of a cylindrical solid pellet (or multiple pellets in parallel) placed between two gas chambers with the flat surfaces exposed to the gases. Two gas streams of known flow rates and dif- 

Wicke-Kallenbach diffusion cell. Gases A and B may be pure gases or gas mixtures. 

---

A diffusion cell method was introduced by Wicke and Kallenbach [3] and therefore is called the Wicke-Kallenbach method. The experimental set up (Figure 5.1) is called the Wicke-Kallenbach cell. It is the most popular method for different diffusion measurements. 

The main advantage of the diffusion cell method is the simplicity of the experimental data treatment. This permits analysis of different transport models to describe experiments with pure gases and with binary and ternary gas mixtures [7,8], As an example... 

The most common method to measure alcohol permeability through membranes is the diffusion cell method under non-stationary conditions. In this method the membrane separates two reservoirs the receptor reservoir containing pure water, and the donor reservoir containing the alcohol solution of known concentration. Usually the alcohol solution in the donor reservoir is refreshed during the experiment to maintain its concentration, Cj, constant along the time. The non-stationary alcohol concentration in the receptor reservoir, c, is followed as a function of time by in situ or ex situ sensors. By integrating Eq. 6.4 the time dependence of is given by... 

The last chapter shows the utility of the time lag method and its applications in the characterization of diffusion and adsorption of pure component systems. In this chapter we address the diffusion cell method, which is used mainly with systems containing two solutes. The process involves the counter-diffusion of these two solutes through a porous medium from one chamber to the other. Usually both of these chambers are open, but there are applications where one of the chambers is a closed chamber. There are two modes of operation of the diffusion cell method. One is the steady state diffusion cell, and the other is the transient diffusion cell. 

The steady state diffusion cell method, despite its simplicity in operation and measurement, does not give us information about the dead-end pores. The information about the dead-end pores is important in two respects ... 

When the system equations are linear (that is when the adsorption isotherm is linear or the system is perturbed incrementally), we can apply the method of Laplace transform to solve the set of equations and obtain the inverse by either the method of residues or a numerical inversion scheme. For the two types of input, the impulse and the square input, the inversion is not necessary if we are interested in using the response to extract the system parameters. If this is our goal which is the case for the diffusion cell method, then the method of moment can be useful for this purpose. 

The utility of the transient diffusion cell is not just useful for the study of a diffusion process involving a non-adsorbing gas, it can be used to study adsorption systems as well. Let us illustrate this with the case of pellet with dead-end pores of a size such that two forms of molecule (that is free and adsorbed molecules) are possible. In this case the mass balance equations describing the concentration distribution in the particle are given in eqs. (13.2-32) to (13.2-35). Usually when the diffusion cell method is used to extract parameters, conditions are chosen such that the adsorption isotherm is linear. Thus, the equilibrium relation of eq. (13.2-34) becomes ... 

Chapters 9 to 11 deal with the dynamic analysis of a single particle exposed to a constant bulk environment. The method of differential adsorption bed discussed in Chapter 11 is suitable for the application of the single particle analysis. A permeation method called the time lag method is useful for characterisation of diffusional flow, viscous flow and surface flow of pure gas through a single pellet (Chapter 12). The diffusion cell method either in steady state mode or transient mode is useful to characterize binary diffusional systems (Chapter 13). All these methods evolve around the analysis of a single particle and they complement each other in the characterization of diffusion and adsorption characteristics of a system. From the stand point of system set-up, the time lag and diffusion cell methods require a careful mounting of a particle or particles between two chambers and extreme care is exercised to avoid any gas by-passing the particle. 

PEM for DMFC is mainly characterized with ionic conductivity and methanol crossover. Ionic conductivity is tested with the four-point probe method. Through plane and in plane ionic conductivity is characterized with temperature and humidity [22]. Methanol crossover can be measured with diffusion cell method, pervapora-tion of methanol solution, dictating of CO amount from cathode out stream [23]. An oxidant-impermeable property is also one of the important factors in PEM for DMFC. The properties of PEM in DMFC are also characterized with an interfacial resistance, an electro-osmotic drag, methanol crossover through MEA, and so on. In this chapter, development of PEM for DMFC are discussed. Approaches for PEM in DMFC are classified as fluorinated polymer, hydrocarbon polymer, modification of polymer materials, and the technical approaches are described as well. 

Two main methods were used for fuel permeability determination ex situ and in situ methods. The former method, also named diffusion cell method, was mostly used for methanol permeability measurements [22,84,85]. In this measurement, a diffusion cell was used, consisting of two reservoirs of distinct composition, with a sample membrane between them. The membrane acts as a parting plane to prevent liquid passing through directly and only permit permeation of the molecules in solution. The two reservoirs were injected with aqueous methanol solution with a certain... 

However, this diffusion cell method was just a simulation of the situation of fuel ceU operation. In situ measurement is a more accurate method that determines fuel concentration during fuel cell operation. Hydrogen or oxygen permeation was usually detected using this method by chronoamperometry [88-91]. Before the measuranent. 

Fluorine. Fluorine is the most reactive product of all electrochemical processes (63). It was first prepared in 1886, but important quantities of fluorine were not produced until the early 1940s. Fluorine was required for the production of uranium hexafluoride [7783-81 -5] UF, necessary for the enrichment of U (see DIFFUSION SEPARATION METHODS). The Manhattan Project in the United States and the Tube Alloy project in England contained parallel developments of electrolytic cells for fluorine production (63). The principal use of fluorine continues to be the production of UF from UF. ... 

Approaches used to model ozone formation include box, gradient transfer, and trajectoty methods. Another method, the particle-in-cell method, advects centers of mass (that have a specific mass assigned) with an effective velocity that includes both transport and dispersion over each time step. Chemistry is calculated using the total mass within each grid cell at the end of each time step. This method has the advantage of avoiding both the numerical diffusion of some gradient transfer methods and the distortion due to wind shear of some trajectory methods. 

Several investigators have used the two-chamber diffusion cell configuration. This experimental method has been found useful to determine diffusion coefficients [11] and to study drug transport from drug delivery devices [12],... 

An analysis of the Poison cell method [4] is instructive. The concentration of the diffusant, C(t), in the receptor column of length h is measured at time t,... 

Side-by-side diffusion cell (membrane method) Diffusion coefficient determination mass transport studies 10-14... 

Diffusion cell for heterogeneous systems (membrane method) Mass transport studies from emulsions 18... 

Diffusion cell for gels (free boundary method) Mass transport studies from water-miscible gels 19... 

As described previously in this chapter, efforts have been made to develop methods for quantification of skin permeability, validation of diffusion cell setups, and correlation of in vitro data with the in vivo situation. However, the average drug permeation experiment does not provide insight into the temporal and local disposition within the tissue, that is, the skin penetration. The following discussion will give an overview of methods tackling this kind of problem. 

F. Netzlaff, K.-H. Kostka, C.-M. Lehr, and U. F. Schaefer. TEWL measurements as a routine method for evaluating the integrity of epidermis sheets in static Franz type diffusion cells in vitro. Limitations shown by transport data testing. Em J. Pharm. Biopharm. 63 44—50 (2006). 

OECD has adopted an in vitro test for skin absorption potential (OECD TG 428, Skin Absorption In Vitro Method). According to this guideline, excised skin from human or animal sources can be used. The skin is positioned in a diffusion cell consisting of a donor chamber and a receptor chamber, between the two chambers. The test substance, which may be radio-labeled, is applied to the surface of the skin sample. The chemical remains on the skin for a specified time under specified conditions, before removal by an appropriate cleansing procedure. The fluid in the receptor chamber is sampled at time points throughout the experiment and analyzed for the test chemical and/or metabolites. 

The diffusion equation is a useful and convenient equation to describe mixing in environmental flows, where the boundaries are often not easily defined. It also lends itself to analytical solutions and is fairly straightforward in numerical solutions. Although there is an alternative technique for solutions to mixing problems (the mixed cell method described in Chapter 6), there are complications of this alternative technique when applied to multiple dimensions and to flows that vary with space and time. Finally, we are comfortable with the diffusion equation, so we would prefer to use that to describe turbulent mixing if possible. 

Deff can be measured, either directly by the flux through a catalyst pellet (Wicke-Kallenbach diffusion cell [60]), or by transient pulse method [61]. It is easier, but less accurate, to relate Deff to molecular diffusivity. 

Various techniques are available for determining the effective diffusivity of solute in gel (Itamunoala, 1988). One of the most reliable techniques is the thin-disk method which uses a diffusion cell with two compartments divided by a thin gel. Each compartment contains a well-stirred solution with different solute concentrations. Effective diffusivity can be calculated from the mass flux verses time measurement (Hannoun and Stephanopoulos, 1986). A few typical values of effective diffusivities are listed in Table 3.2. 

The traditional methods for evaluation of the delivery and metabolism of exogenous materials in skin involve the use of diffusion cells and/or tape stripping followed by HPLC and mass spectrometry. These methods involve modification of the skin, provide no spatial information, and may alter skin transport properties. In this section, both the permeation and metabolism of a-TAc are monitored inside skin with confocal Raman microscopy. 

---