Diffiisivity effective

CO bonding to the active sites and difficult product desorption vide infra). In contrast, the peak current density of methanol oxidation decreases with the scan rate (Fig. 14c), even by increasing the concentration of MeOH from 10 to 20 wt%, in an attempt of magnifying the diffiision effects. Apparently, the diffusion of MeOH across the MWCNT support is veiy fast but the electrocatalyst is not sufficiently active and the peak current density decreases by increasing the scan rate. 

For short times, where diffiision effects have not reached the end of the cell, the Boltzmann transformation is used to yield an expression for the diffiisivity at concentration... 

More complex empirical equations based on Equation 1.155 have also been developed. For example, Amphlett et al. [167] presented empirical equations and terms that relate activation losses, internal resistance, and all temperature dependencies through fitting parameters. Sena et at. [168] analyzed the catalyst layer and considered it as a thin-film flooded agglomerate thus, the GDE is assumed to be formed by an assembly of flooded zones (catalytic zones) and empty zones (no catalyst present). The final equation relates the oxygen diffiision effects in the GDE ... 

The introductory remarks about unimolecular reactions apply equivalently to bunolecular reactions in condensed phase. An essential additional phenomenon is the effect the solvent has on the rate of approach of reactants and the lifetime of the collision complex. In a dense fluid the rate of approach evidently is detennined by the mutual difhision coefficient of reactants under the given physical conditions. Once reactants have met, they are temporarily trapped in a solvent cage until they either difhisively separate again or react. It is conmron to refer to the pair of reactants trapped in the solvent cage as an encounter complex. If the unimolecular reaction of this encounter complex is much faster than diffiisive separation i.e., if the effective reaction barrier is sufficiently small or negligible, tlie rate of the overall bimolecular reaction is difhision controlled. 

There is one important caveat to consider before one starts to interpret activation volumes in temis of changes of structure and solvation during the reaction the pressure dependence of the rate coefficient may also be caused by transport or dynamic effects, as solvent viscosity, diffiision coefficients and relaxation times may also change with pressure [2]. Examples will be given in subsequent sections. 

R), i.e. there is no effect due to caging of the encounter complex in the common solvation shell. There exist numerous modifications and extensions of this basic theory that not only involve different initial and boundary conditions, but also the inclusion of microscopic structural aspects [31]. Among these are hydrodynamic repulsion at short distances that may be modelled, for example, by a distance-dependent diffiision coefficient... 

Many additional refinements have been made, primarily to take into account more aspects of the microscopic solvent structure, within the framework of diffiision models of bimolecular chemical reactions that encompass also many-body and dynamic effects, such as, for example, treatments based on kinetic theory [35]. One should keep in mind, however, that in many cases die practical value of these advanced theoretical models for a quantitative analysis or prediction of reaction rate data in solution may be limited. 

FIG. 16-13 Effect of Re Sc group, distribution ratio, and diffiisivity ratio on height of a transfer unit. Dotted hnes for gas and sohd hnes for liquid-phase systems. 

Pore diffusion limitation was studied on a very porous catalyst at the operating conditions of a commercial reactor. The aim of the experiments was to measure the effective diffiisivity in the porous catalyst and the mass transfer coefficient at operating conditions. Few experimental results were published before 1970, but some important mathematical analyses had already been presented. Publications of Clements and Schnelle (1963) and Turner (1967) gave some advice. 

A striking example of the interaction of solution velocity and concentration is given by Zembura who found that for copper in aerated 0-1 N H2SO4, the controlling process was the oxygen reduction reaction and that up to 50°C, the slow step is the activation process for that reaction. At 75 C the process is now controlled by diffiision, and increasing solution velocity has a large effect on the corrosion rate (Fig. 2.5), but little effect at temperatures below 50 C. This study shows how unwise it is to separate these various... 

Undoped, Mn, and Pr-doped ZnS namopartides synthesized by wet chemiral mdhod were optically annealed in air or vacuum. PL emission inoeas with annulling time. This increase is attributed to the photo-oxidation, enhancanent in the crystal quality, and diffiision of the luminescent ions. PL intensity of nanoparticles annealed in air increased more significantly due to the photo-oxidation compared with the nanoparticles annealed in vacuum. Mn and Pr-codoped ZnS nanoparticles emitted white light due to the effects of dopants. The optical annealing enhanced the emission intensity. 

A. Mohoric, J. Stepisnik 2000, (Effect of natural convection in a horizontally oriented cylinder on NMR imaging of the distribution of diffiisivity), Phys. Rev. E 62, 6628. 

Effects of isotopic mass on molecular and atomic velocities and diffiisivity... 

Saffman, P. G. (1960). On the effect of molecular diffiisivity in turbulent diffusion. J. Fluid Mech. 8, 273-283. 

A reactant of bulk concentration Cao reacts on the external surface of catalyst spheres of radius 7 in a slurry reactor. The first-order surface reaction rate coefficient is k , and the diffiisivity of A in the solution is Da- Find fhe effective rate coefficient in terms of these quantities, assuming that stirring is sufficiently slow that fhe fluid around particles is stagnant. 

In equations 5-8, the variables and symbols are defined as follows p0 is reference mass density, v is dimensional velocity field vector, p is dimensional pressure field vector, x is Newtonian viscosity of the melt, g is acceleration due to gravity, T is dimensional temperature, tT is the reference temperature, c is dimensional concentration, c0 is far-field level of concentration, e, is a unit vector in the direction of the z axis, Fb is a dimensional applied body force field, V is the gradient operator, v(x, t) is the velocity vector field, p(x, t) is the pressure field, jl is the fluid viscosity, am is the thermal diffiisivity of the melt, and D is the solute diffiisivity in the melt. The vector Fb is a body force imposed on the melt in addition to gravity. The body force caused by an imposed magnetic field B(x, t) is the Lorentz force, Fb = ac(v X v X B). The effect of this field on convection and segregation is discussed in a later section. 

The treatment can be modified to include effects of the temperature development and tilting of the susceptor by using the temperature dependence of the diffiision coefficient and adjusting d and (191). In this manner, the experimental data can be correlated, but the model has limited capability for predicting behavior beyond the particular set of experiments used to fit the model. In fact, because of the low values of the Reynolds number (<50) in typical horizontal CVD reactors, film theory and simple... 

In n-p structures formed by sequential diffiisions of B and P, dislocation climb occurred at the same time that the emitter-push effect was seen in the B layer (23). This result implies that the same point defect is responsible for both phenomena. 

The deactivation of cracking catalysts by coking with vacuum gas oils (VGO) is studied in relation to the chemical deactivation due to site coverage, and with the increase of diffusional limitations. These two phenomena are taken into account by a simple deactivation function versus catalyst coke content. The parameters of this function arc discussed in relation to feedstock analysis and change of effective diffiisivity with catalyst coke content. 

When the operating pressure is higher than the critical pressure of the reactant mixture, no obvious effect of the reaction pressure on deactivation is observed as shown in Figure 4, though a higher pressure is seemingly harmful, probably because the diffiisivity under a high pressure is lower. 

It can be anticipated that prediction of diffiisivities should be best with larger particles since the diffusion path is physically longer. A few simulation runs with different values of diffusivity, solubility and external mass transfer coefficient, show that the most sensitive parameter (or resistance) are intraparticle diffusivity and solubility while the effect of external mass transfer coefficient is small. 

The effective diffiisivities of DCB in SC C02 for these runs are optimized to De = 4 10 9 m /s. The corresponding tortuosity factors amount to Dm/Dc = 2.3 and 2.5 when estimating the molecular diffusivity by means of the correlation of [10]. These values are in reasonable agreement with respect to those found in the literature. For example in a related study of... 

The cage or window effect was proposed by Gorring (48) to explain the nonlinear effect of chain length observed in hydrocracking of various n alkanes over T zeolite, chabazite (CHA) and erionite (ERI). Thus, when a nC22 alkane is cracked over erionite, there are two maxima in the size distribution of the product molecules at carbon numbers of 4 and 11 and a minimum at carbon number of 8. The diffiisivities of n-alkanes also change in a similar periodic manner by over two orders of magnitude between the minimum at C8 and the maxima. This shows that for diffusion, and hence for shape selective effects, not only the size but also the structure of the reactant and product molecules need to be considered. 

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