Transport mechanisms surface diffusion

The research group led by Dr. Djilali at the University of Victoria has developed an ex situ experimental technique using fluorescent microscopy to study the liquid water transport mechanisms inside diffusion layers and on their surfaces [239-243]. The diffusion layer is usually placed between two plates (the top plate may or may not have a channel) the liquid water, which is pumped through a syringe pump, flows from the bottom plate through the DL. Fluorescein dye is added to the water for detection with the microscope. 

In this context, to describe the position dependence of the model species, it is important to take in mind that, in electrochemical wastewater-treatment processes, it can be assumed that in the treated wastewater there is always enough supporting electrolyte to minimize the migration of electroactive species. Hence the primary mass-transport mechanisms are diffusion and convection. Hence, the mass balance of a volume element assuming that reactions are restricted to the electrode surface takes the form of (4.2). 

A mechanism has been postulated to account for the growth of filamentous carbon produced from metal catalyzed decomposition of acetylene ( 5, 6). This mechanism, which is outlined in the schematic diagram, Figure 2, involves the diffusion of carbon through the catalyst particle from the hotter leading face, on which exothermic decomposition of the hydrocarbon occurs, to the cooler trailing faces, at which carbon is deposited from solution. Excess carbon buildup occurs at the exposed particle face and is transported by surface diffusion around the peripheral surfaces of the particle to form an outer skin on the filament. 

K). The changes in slope indicate changes in the mechanism of surface diffusion. While, at low temperatures, adatom diffusion or adatom-surface atom exchange appears to be the dominant atom-transport mechanism, the diffusion of surface vacancies created by thermal roughening is likely to be dominant at high temperatures to account for the increased activation energies. For example, copper adatom and vacancy diffusion rates in the Cu(l 10) crystal face are given by... 

Besides electrokinetic transport, chemical reactions also occur at the electrode surfaces (i.e., water electrolysis reactions with production of at the anode and OH at the cathode). Common mass-transport mechanisms like diffusion or convection and physical and chemical interactions of the species with the medium also occur. In a low-permeable porous medium under an electrical field, the major transport mechanism through the soil matrix during treatment for nonionic chemical species consists mainly of electro-osmosis, electrophoresis, molecular diffusion, hydrodynamic dispersion (molecular diffusion and dispersion varying with the heterogeneity of soils and fluid velocity [8]), sorption/ desorption, and chemical or biochemical reactions. Since related experiments are conducted in a relatively short period of time, the chemical and biochemical reactions that occur in the soil water are neglected [9]. 

Structure and water sorption characteristics of fuel cell media determine their transport properties. The dynamic properties of water determine microscopic transport mechanisms and diffusion rates of protons in PEM and CLs. Protons must be transported at sufficiently high rates, away from or toward the active Pt catalyst in anode and cathode catalyst layers, respectively. Effective rates of proton transport in nanoporous PEM and CLs result from a convolution of microscopic transport rates of protons with random network properties of aqueous pathways. Accounting for the geometry of these materials, namely, their external surface area and thickness, gives their resistances. 

The significance of the results presented in Figs. 43 5 is that they allow one to estimate the area over the surface where the flux (transfer rate) become uniform. The mass-transfer-rate constant (reduced flux) measured in this uniformly accessible area and referred to as A is of a particular significance because it can be analyzed theoretically in a much more efficient way than the local flux. Moreover, A can be directly used for determining the significance of various transport mechanisms like diffusion, interception, specific or external force, and so forth. 

The concentration boundary layer forms because of the convective transport of solutes toward the membrane due to the viscous drag exerted by the flux. A diffusive back-transport is produced by the concentration gradient between the membranes surface and the bulk. At equiUbrium the two transport mechanisms are equal to each other. Solving the equations leads to an expression of the flux ... 

In either equation, /c is given by Eq. (16-84) for parallel pore and surface diffusion or by Eq. (16-85) for a bidispersed particle. For nearly linear isotherms (0.7 < R < 1.5), the same linear addition of resistance can be used as a good approximation to predict the adsorption behavior of packed beds, since solutions for all mechanisms are nearly identical. With a highly favorable isotherm (R 0), however, the rate at each point is controlled by the resistance that is locally greater, and the principle of additivity of resistances breaks down. For approximate calculations with intermediate values of R, an overall transport parameter for use with the LDF approximation can be calculated from the following relationship for sohd diffusion and film resistance in series... 

We have so far assumed that the atoms deposited from the vapor phase or from dilute solution strike randomly and balHstically on the crystal surface. However, the material to be crystallized would normally be transported through another medium. Even if this is achieved by hydrodynamic convection, it must nevertheless overcome the last displacement for incorporation by a random diffusion process. Therefore, diffusion of material (as well as of heat) is the most important transport mechanism during crystal growth. An exception, to some extent, is molecular beam epitaxy (MBE) (see [3,12-14] and [15-19]) where the atoms may arrive non-thermalized at supersonic speeds on the crystal surface. But again, after their deposition, surface diffusion then comes into play. 

When a polymer film is exposed to a gas or vapour at one side and to vacuum or low pressure at the other, the mechanism generally accepted for the penetrant transport is an activated solution-diffusion model. The gas dissolved in the film surface diffuses through the film by a series of activated steps and evaporates at the lower pressure side. It is clear that both solubility and diffusivity are involved and that the polymer molecular and morphological features will affect the penetrant transport behaviour. Some of the chemical and morphological modification that have been observed for some epoxy-water systems to induce changes of the solubility and diffusivity will be briefly reviewed. 

The devolatilization of a component in an internal mixer can be described by a model based on the penetration theory [27,28]. The main characteristic of this model is the separation of the bulk of material into two parts A layer periodically wiped onto the wall of the mixing chamber, and a pool of material rotating in front of the rotor flights, as shown in Figure 29.15. This flow pattern results in a constant exposure time of the interface between the material and the vapor phase in the void space of the internal mixer. Devolatilization occurs according to two different mechanisms Molecular diffusion between the fluid elements in the surface layer of the wall film and the pool, and mass transport between the rubber phase and the vapor phase due to evaporation of the volatile component. As the diffusion rate of a liquid or a gas in a polymeric matrix is rather low, the main contribution to devolatilization is based on the mass transport between the surface layer of the polymeric material and the vapor phase. 

Inspection of Fig. 15.3 reveals that while for jo 0.1 nAcm , the effectiveness factor is expected to be close to 1, for a faster reaction with Jo 1 p,A cm , it will drop to about 0.2. This is the case of internal diffusion limitation, well known in heterogeneous catalysis, when the reagent concentration at the outer surface of the catalyst grains is equal to its volume concentration, but drops sharply inside the pores of the catalyst. In this context, it should be pointed out that when the pore size is decreased below about 50 nm, the predominant mechanism of mass transport is Knudsen diffusion [Malek and Coppens, 2003], with the diffusion coefficient being less than the Pick diffusion coefficient and dependent on the porosity and pore stmcture. Moreover, the discrete distribution of the catalytic particles in the CL may also affect the measured current owing to overlap of diffusion zones around closely positioned particles [Antoine et ah, 1998]. 

Surface diffusion is yet another mechanism that is often invoked to explain mass transport in porous catalysts. An adsorbed species may be transported either by desorption into the gas phase or by migration to an adjacent site on the surface. It is this latter phenomenon that is referred to as surface diffusion. This phenomenon is poorly understood and the rate of mass... 

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