Gas diffusion models

Hence not only for numerical neutral gas diffusion models , but also for such hybrid Monte Carlo techniques internally consistent expressions for the i 0 1 integrals, for (/ = 0,1,2) must be computed. These fits should then, again, preferentially be given in terms of ln(Teff)-... 

GONGENTRATIONS OF EXGHANGEABLE G PER VOLUME OF UNSATURATED ZONE Goupling of geochemical and gas diffusion models requires common units of concentration for all... 

Coal particle gas diffusion mathematical model was set up basing on the third boundary condition and taking into account gas mass transmission characteristics on borderline. The applying scope includes gas diffusion model under the first boundary condition, thus it is not only more scientific and reasonable, but also is provided with application more widely. 

Maxwell Binary gas diffusivity model in porous media... 

An important advancement in carburizing has been the development of diffusion models to calculate the carbon gradient as a function of time as the gas composition and temperature change (13). Such models can be coupled with computer control of the gas composition and temperature to produce desired carbon profiles. 

The Shei wood-number relation for gas-phase mass-transfer coefficients as represented by the film diffusion model in Eq. (5-286) can be rearrangecTas follows ... 

Kramers and Alberda (K20) have reported some data in graphical form for the residence-time distribution of water with countercurrent air flow in a column of 15-cm diameter and 66-cm height packed with 10-mm Raschig rings. It was concluded that axial mixing increased with increasing gas flow rate and decreasing liquid flow rate, and that the results were not adequately represented by the diffusion model. 

More disagreement exists with respect to axial dispersion—for example, regarding the applicability of the diffusion model, and regarding the influence of gas and liquid flow rates. More work on these aspects and on the influence of fluid distribution and method of packing is required. Some of the available results are compared in Fig. 3. 

Tadaki and Maeda (Tl) examined the desorption of carbon dioxide from water in a bubble-column and analyzed the experimental results under the assumption that while the gas phase moves in piston flow, the liquid undergoes axial mixing that can be characterized by the diffusion model. (Shulman and Molstad, in contrast, assumed piston flow for both phases.) Only poor agreement was obtained between the theoretical model and the experimental... 

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. 

Substituting Eq. (1.92) into Eq. (2.70), we obtain spectra proper to the gas phase at k < 1. These spectra for t = 1 are depicted in Fig. 2.6. There co for the IR spectra is measured from the vibrational frequency and only the right-hand half of the symmetrical band is shown. The spectra deviate only slightly from those arising in the J-diffusion model. It is hardly possible to see that their wings are not Lorentzian. The effect... 

The concentration of gas over the active catalyst surface at location / in a pore is ai [). The pore diffusion model of Section 10.4.1 linked concentrations within the pore to the concentration at the pore mouth, a. The film resistance between the external surface of the catalyst (i.e., at the mouths of the pore) and the concentration in the bulk gas phase is frequently small. Thus, a, and the effectiveness factor depends only on diffusion within the particle. However, situations exist where the film resistance also makes a contribution to rj so that Steps 2 and 8 must be considered. This contribution can be determined using the principle of equal rates i.e., the overall reaction rate equals the rate of mass transfer across the stagnant film at the external surface of the particle. Assume A is consumed by a first-order reaction. The results of the previous section give the overall reaction rate as a function of the concentration at the external surface, a. ... 

Figure 15.2 Schematic representation of different electrochemical cell types used in studies of electrocatalytic reactions (a) proton exchange membrane single cell, comprising a membrane electrode assembly (b) electrochemical cell with a gas diffusion electrode (c) electrochemical cell with a thin-layer working electrode (d) electrochemical cell with a model nonporous electrode. CE, counter-electrode RE, reference electrode WE, working electrode.

A much more detailed and time-dependent study of complex hydrocarbon and carbon cluster formation has been prepared by Bettens and Herbst,83 84 who considered the detailed growth of unsaturated hydrocarbons and clusters via ion-molecule and neutral-neutral processes under the conditions of both dense and diffuse interstellar clouds. In order to include molecules up to 64 carbon atoms in size, these authors increased the size of their gas-phase model to include approximately 10,000reactions. The products of many of the unstudied reactions have been estimated via simplified statistical (RRKM) calculations coupled with ab initio and semiempirical energy calculations. The simplified RRKM approach posits a transition state between complex and products even when no obvious potential barrier... 

Gas diffusion in the nano-porous hydrophobic material under partial pressure gradient and at constant total pressure is theoretically and experimentally investigated. The dusty-gas model is used in which the porous media is presented as a system of hard spherical particles, uniformly distributed in the space. These particles are accepted as gas molecules with infinitely big mass. In the case of gas transport of two-component gas mixture (i = 1,2) the effective diffusion coefficient (Dj)eff of each of the... 

The terms Jga and Jsa are the diffusive fluxes of species a in the gas and solid phases, respectively. Note that in addition to molecular-scale diffusion, these terms include dispersion due to particle-scale turbulence. The latter is usually modeled by introducing a gradient-diffusion model with an effective diffusivity along the lines of Eqs. (149) and (151). Thus, for large particle Reynolds numbers the molecular-scale contribution will be negligible. The term Ma is the... 

A mathematical model is described [138] in which the self-heating of material layers under industrial conditions is simulated. The model takes into account oxygen (or gas) diffusion and consumption, reactant conversion, heat conduction in, and heat transfer to and from the layer. Scale-up experiments were performed which showed the model can be successfully applied to predict the self-heating phenomenon in the layers. 

Nooren, P. A., H. A. Wouters, T. W. J. Peeters, D. Roekaerts, U. Maas, and D. Schmidt (1997). Monte Carlo PDF modelling of a turbulent natural-gas diffusion flame. 

T. Koido, T. Furusawa, and K. Moriyama. An approach to modeling two-phase transport in the gas diffusion layer of a proton exchange membrane fuel cell. Journal of Power Sources 175 (2008) 127-136. 

O. Ghapuis, M. Prat, M. Quintard, et al. Two-phase flow and evaporation in model fibrous media Application to the gas diffusion layer of PEM fuel cells. Journal of Power Sources 178 (2008) 258-268. 

The simplest practicable approach considers the membrane as a continuous, nonporous phase in which water of hydration is dissolved.In such a scenario, which is based on concentrated solution theory, the sole thermodynamic variable for specifying the local state of the membrane is the water activity the relevant mechanism of water back-transport is diffusion in an activity gradient. However, pure diffusion models provide an incomplete description of the membrane response to changing external operation conditions, as explained in Section 6.6.2. They cannot predict the net water flux across a saturated membrane that results from applying a difference in total gas pressures between cathodic and anodic gas compartments. 

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