Bulk transport coefficient

The extracted parameters are vital for rationalizing mechanisms and amounts of water fluxes in PEFCs. The model could be applied for the analysis of sorption data at varying PEM thickness and equilibrium water content. Experiments running at varying T would provide activation energies of the vaporization-exchange rate constant and bulk transport coefficients. Similar modeling tools can be developed for the study of water sorption and fluxes in catalyst layers. They can be extended, furthermore,... 

Ordinary or bulk diffusion is primarily responsible for molecular transport when the mean free path of a molecule is small compared with the diameter of the pore. At 1 atm the mean free path of typical gaseous species is of the order of 10 5 cm or 103 A. In pores larger than 1CT4 cm the mean free path is much smaller than the pore dimension, and collisions with other gas phase molecules will occur much more often than collisions with the pore walls. Under these circumstances the effective diffusivity will be independent of the pore diameter and, within a given catalyst pore, ordinary bulk diffusion coefficients may be used in Fick s first law to evaluate the rate of mass transfer and the concentration profile in the pore. In industrial practice there are three general classes of reaction conditions for which the bulk value of the diffusion coefficient is appropriate. For all catalysts these include liquid phase reactions... 

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) ... 

The coefficient of bulk viscosity is of importance only in compressible flow, as may be seen from Eq. (7). This transport coefficient has been studied only slightly and is not further considered here the subject has been reviewed by Karim and Rosenhead (Kl) and has been considered further in a recent symposium under the leadership of Rosenhead (R5). 

We see from Figure 3-1 that edge dislocations possess a compressed region above, and a dilated region below the glide plane. Therefore, in the dilated area around the dislocation line, the transport coefficients will be larger than in the bulk crystal. Thus, dislocations can serve as fast diffusion pipes for atomic transport. 

The influence of plastic deformation on the reaction kinetics is twofold. 1) Plastic deformation occurs mainly through the formation and motion of dislocations. Since dislocations provide one dimensional paths (pipes) of enhanced mobility, they may alter the transport coefficients of the structure elements, with respect to both magnitude and direction. 2) They may thereby decisively affect the nucleation rate of supersaturated components and thus determine the sites of precipitation. However, there is a further influence which plastic deformations have on the kinetics of reactions. If moving dislocations intersect each other, they release point defects into the bulk crystal. The resulting increase in point defect concentration changes the atomic mobility of the components. Let us remember that supersaturated point defects may be annihilated by the climb of edge dislocations (see Section 3.4). By and large, one expects that plasticity will noticeably affect the reactivity of solids. 

The mass transport limiting current is the maximum current (or rate) that the process can achieve. In order to increase its value, an increase of the electrode area, bulk concentration, or mass transport coefficient is needed. In the last case, this means a decrease of the diffusion layer thickness which can be done, for example, by forced convection. 

From the voltammograms of Fig. 5.12, the evolution of the response from a reversible behavior for values of K hme > 10 to a totally irreversible one (for Kplane < 0.05) can be observed. The limits of the different reversibility zones of the charge transfer process depend on the electrochemical technique considered. For Normal or Single Pulse Voltammetry, this question was analyzed in Sect. 3.2.1.4, and the relation between the heterogeneous rate constant and the mass transport coefficient, m°, defined as the ratio between the surface flux and the difference of bulk and surface concentrations evaluated at the formal potential of the charge transfer process was considered [36, 37]. The expression of m° depends on the electrochemical technique considered (see for example Sect. 1.8.4). For CV or SCV it takes the form... 

Figure 6 shows the influence of the bulk diffusion coefficient, Dhi on the metal deposition profiles. Obviously, by decreasing the diffusivity the metal deposition process becomes more diffusion rate-determined. With decreasing diffusivity the transport of reactant and intermediates is decreased resulting in a less deep penetration into the catalyst pellet. Therefore, the metal deposition maximum is shifted further to the exterior of the catalyst pellet. 

It should also be mentioned that the appearance of the reversible behavior depends on the relative value of ks and mass transport coefficient (km), since no equilibrium exists between the surface and bulk concentrations, reactants are continuously transported to the electrode surface by mass transport (- diffusion). 

Extended nonequilibrium thermodynamics is not based on the local equilibrium hypothesis, and uses the conserved variables and nonconserved dissipative fluxes as the independent variables to establish evolution equations for the dissipative fluxes satisfying the second law of thermodynamics. For conservation laws in hydrodynamic systems, the independent variables are the mass density, p, velocity, v, and specific internal energy, u, while the nonconserved variables are the heat flux, shear and bulk viscous pressure, diffusion flux, and electrical flux. For the generalized entropy with the properties of additivity and convex function considered, extended nonequilibrium thermodynamics formulations provide a more complete formulation of transport and rate processes beyond local equilibrium. The formulations can relate microscopic phenomena to a macroscopic thermodynamic interpretation by deriving the generalized transport laws expressed in terms of the generalized frequency and wave-vector-dependent transport coefficients. 

Nicolis, G., and G. Severne Nonstationary Contributions to the Bulk Viscosity and other Transport Coefficients. J. Chem. Phys. 44, 1477—1486 (1966). 

Our results clearly indicate that the EMD transport coefficient does include the viscous part, despite the absence of imposed bulk flow, contradicting earlier assertions [5,11] discussed above. This is rationalised if cross-sectional equilibrium of the streaming velocity and density profiles is attained. Evidence of the latter is provided in the inset in Figure 2 for a pore density of 5.95 nm at 150 K. 

It is also straightforward to extend the equations to allow for only partial equihbration during transport. Iwamori (1993a) presents a one-dimensional steady-state single-porosity model for stable elements that includes diffusive re-equili-bration between melt and solid. He does not extend it to radioactive nuclides in this paper but includes this effect in his two porosity model (Iwamori, 1994) (see Section 3.14.4.3.4). The expected effects of chemical disequilibrium should be similar to those in the Qin (1992) dynamic melting model, namely he effective bulk partition coefficients of all elements will be driven towards unity. 

Additional information E ea though this reaction is a solid catalytic reaction, we will make use of the brrlk catalyst density in order to write oiu balarrces in terms of reactor volrrme rather than catalyst weight (recall = r APi,)- For the bulk catalyst density of p. =1.5 g/cm and a 2-cm inside diameter of the tube contain-irrg the catalyst pellets, the specific reaction rate, ft, and the transport coefficient, ft, are ft = 0.7 min" and ft = 0.2 min , respectively. 

The resistances to the mass transport that a species encounters when is transferred from the gas to the hquid phase are reported in Figure 38.3. Gas and liquid phases contribute to the overall resistance because of the formation of boundary layers close to the membrane surface. This imphes that the concentration of a generic species i in the bulk of the two phases is different from its concentration at the membrane surfaces. The resistance offered by the membrane with gas-filled pores will be different (generally lower) than that with liquid-filled pores, due to the different effective diffusion coefficients. The overall mass-transport coefficient is given by... 

The treatment of LRT for confined fluids proceeds in the same fashion as that for deriving transport coefficients of bulk fluids. " "We consider a fluid confined between two planar surfaces (or walls ) at equilibrium at t = 0. The surfaces are parallel to the xz plane. 

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