Transport diffusion desorption

With this information in mind, we can construct a model for the deposition rate. In the simplest case, the rate of flux of reactants to the surface (step 2) is equal to the rate at which the reactants are consumed at steady state (step 5). All other processes (decomposition, adsorption, surface diffusion, desorption, and transport away from the substrate) are assumed to be rapid. It is generally assumed that most CVD reactions are heterogeneous and first order with respect to the major reactant species, such that a general rate expression of the form of Eq. (3.2) would reduce to... 

Grathwohl, P. (1998). Diffusion in natural porous media contaminant transport, sorption/desorption and dissolution kinetics, Kluwer Publishers, Boston, MA. 

The adsorption-surface diffusion-desorption mechanism of transport through the SSF membrane can simultaneously provide high separation selectivity between H2 and the impurities of the PSA waste gas and high flux for the impurities even when the gas pressure in the high-pressure side of the membrane is low to moderate (3-5 atm). 

Figure 6 provides a comparison between measured spectra and theoretical spectra calculated under the assumption that the adsorption/desorption process is controlled by either intracrystalline diffusion (Fig. 6a) or external transport resistances such as surface barriers (Fig. 6b). For simplicity in the calculations, the crystallites have been assumed to be of nearly spherical shape with a concentration-independent transport diffusivity Dj or surface permeability a, respectively. Values of the intracrystalline mean lifetime are therefore given by...

Eq. 21 with Eq. 23 results as the solution of the corresponding differential equation of normal diffusion with the appropriate initial and boundary conditions. These relations hold with the adequate interpretation of D as a self-diffusivity or a transport diffusivity, respectively, for both tracer exchange between the initially adsorbed species A by species B and the relative uptake in an adsorption experiment. It should be noted that Eq. 21 also describes the molecular uptake by single-file systems, since with respect to adsorption/desorption there are no differences between single-file systems and systems which permit normal diffusion. 

Grathwohl, P. (1998) Diffusion in Natural Porous Media Contaminant Transport, Sorption, Desorption and Dissolution Kinetics, Kluwer Academic Publishers. 

The detailed information on initial and boundary conditions can be found in Ref. 115 and references therein. Partial differential equations (PDEs) describing processes of diffusion transport, adsorption/desorption, and reaction in the TAP micro-reactor can be solved either analytically or numerically. " Although the analytical solution allows fast estimation of kinetic parameters, the... 

Integration of a H2 PSA process with an adsorbent membrane can meet this goal [23, 24]. A nano-porous carbon adsorbent membrane called Selective Surface Flow (SSF) membrane which selectively permeates CO2, CO and CH4 from their mixtures with H2 by an adsorption- surface diffusion-desorption transport mechanism may be employed for this purpose. The SSF membrane can produce an enriched H2 gas stream from a H2 PSA waste gas, which can then be recycled as feed to the PSA process for increasing the over-all H2 recovery. The membrane is prepared by controlled carbonization of poly-vinyledene chloride supported on a macro-porous alumina tube. The membrane pore diameters are between 6 -7 A, and its thickness is - 1-2 pm [25]. 

Rapid Adsorption-Desorption Cycles For rapid cycles with particle diffusion controlling, when the cycle time is much smaller than the time constant for intraparticle transport, the LDF approximation becomes inaccurate. The generalized expression... 

The role of bulk diffusion in controlling reaction rates is expected to be significant during surface (catalytic-type) processes for which transportation of the bulk participant is slow (see reactions of sulphides below) or for which the boundary and desorption steps are fast. Diffusion may, for example, control the rate of Ni3C hydrogenation which is much more rapid than the vacuum decomposition of this solid. 

Models of chemical reactions of trace pollutants in groundwater must be based on experimental analysis of the kinetics of possible pollutant interactions with earth materials, much the same as smog chamber studies considered atmospheric photochemistry. Fundamental research could determine the surface chemistry of soil components and processes such as adsorption and desorption, pore diffusion, and biodegradation of contaminants. Hydrodynamic pollutant transport models should be upgraded to take into account chemical reactions at surfaces. 

Process Description Pervaporation is a separation process in which a liquid mixture contacts a nonporous permselective membrane. One component is transported through the membrane preferentially. It evaporates on the downstream side of the membrane leaving as a vapor. The name is a contraction of permeation and evaporation. Permeation is induced by lowering partial pressure of the permeating component, usually by vacuum or occasionally with a sweep gas. The permeate is then condensed or recovered. Thus, three steps are necessary Sorption of the permeating components into the membrane, diffusive transport across the nonporous membrane, then desorption into the permeate space, with a heat effect. Pervaporation membranes are chosen for high selectivity, and the permeate is often highly purified. 

Oxidation of Adsorbed CO The electro-oxidation of CO has been extensively studied given its importance as a model electrochemical reaction and its relevance to the development of CO-tolerant anodes for PEMFCs and efficient anodes for DMFCs. In this section, we focus on the oxidation of a COads monolayer and do not cover continuous oxidation of CO dissolved in electrolyte. An invaluable advantage of COads electro-oxidation as a model reaction is that it does not involve diffusion in the electrolyte bulk, and thus is not subject to the problems associated with mass transport corrections and desorption/readsorption processes. 

This solution is valid for the initially linear portion of the sorption (or desorption) curve when MtIM is plotted against the square root of time. These equations also demonstrate that for Fickian processes the sorption time scales with the square of the dimension. Thus, to confirm Fickian diffusion rigorously, a plot of MJM vs. Vt/T should be made for samples of different thicknesses a single master curve should be obtained. If the data for samples of different thicknesses do not overlap despite transport exponents of 0.5, the transport is designated pseudo-Fickian. ... 

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... 

Durable changes of the catalytic properties of supported platinum induced by microwave irradiation have been also recorded [29]. A drastic reduction of the time of activation (from 9 h to 10 min) was observed in the activation of NaY zeolite catalyst by microwave dehydration in comparison with conventional thermal activation [30]. The very efficient activation and regeneration of zeolites by microwave heating can be explained by the direct desorption of water molecules from zeolite by the electromagnetic field this process is independent of the temperature of the solid [31]. Interaction between the adsorbed molecules and the microwave field does not result simply in heating of the system. Desorption is much faster than in the conventional thermal process, because transport of water molecules from the inside of the zeolite pores is much faster than the usual diffusion process. 

However, there are significant limitations. Sensors made in this may have been universally observed to have limited long-term stability, in the worst cases losing up to 85% sensitivity when stored overnight in buffer, and total loss of activity if allowed to dry out between measurements [56], The decrease is speculated to be due to diffusion of Ru(bpy)32+ into hydrophobic regions of the Nation film restricting charge transport, rather than desorption of Ru(bpy)32+. 

The Mc term can be used to approximate initial sorption or desorption on the glass surface, and the kt1 2 term the longer-term diffusion transport into or out of the surface (3). As shown in Figure 2, the sorption term decreases and the diffusion term increases with temperature for the obsidian experiments. Tabulated values for Equation 1 are presented in Table 1 along with the regression coefficient, r2, for glass data. 

Hoftyzer and van Krevelen [100] investigated the combination of mass transfer together with chemical reactions in polycondensation, and deduced the ratedetermining factors from the description of gas absorption processes. They proposed three possible cases for poly condensation reactions, i.e. (1) the polycondensation takes place in the bulk of the polymer melt and the volatile compound produced has to be removed by a physical desorption process, (2) the polycondensation takes place exclusively in the vicinity of the interface at a rate determined by both reaction and diffusion, and (3) the reaction zone is located close to the interface and mass transport of the reactants to this zone is the rate-determining step. 

During the studies carried out on this process some unusual behavior has been observed. Such results have led some authors to the conclusion that SSP is a diffusion-controlled reaction. Despite this fact, the kinetics of SSP also depend on catalyst, temperature and time. In the later stages of polymerization, and particularly in the case of large particle sizes, diffusion becomes dominant, with the result that the removal of reaction products such as EG, water and acetaldehyde is controlled by the physics of mass transport in the solid state. This transport process is itself dependent on particle size, density, crystal structure, surface conditions and desorption of the reaction products. 

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