Transport external

Transport numbers are intended to measure the fraction of the total ionic current carried by an ion in an electrolyte as it migrates under the influence of an applied electric field. In essence, transport numbers are an indication of the relative ability of an ion to carry charge. The classical way to measure transport numbers is to pass a current between two electrodes contained in separate compartments of a two-compartment cell These two compartments are separated by a barrier that only allows the passage of ions. After a known amount of charge has passed, the composition and/or mass of the electrolytes in the two compartments are analyzed. Erom these data the fraction of the charge transported by the cation and the anion can be calculated. Transport numbers obtained by this method are measured with respect to an external reference point (i.e., the separator), and, therefore, are often referred to as external transport numbers. Two variations of the above method, the Moving Boundary method [66] and the Eiittorff method [66-69], have been used to measure cation (tR+) and anion (tx ) transport numbers in ionic liquids, and these data are listed in Table 3.6-7. 

There is difficulty in defining the absolute mobilities of the constituent ions in a molten salt, since it does not contain fixed particles that could serve as a coordinate reference. Experimental means for measuring external transport numbers or external mobilities are scarce, although the zone electromigration method (layer method) and the improved Hittorf method may be used. In addition, external mobilities in molten salts cannot be easily calculated, even from molecular dynamics simulation. 

Na oi and was partially blocked by amiloride but not by cimetidine. Since these investigators also found that amiloride and cimetidine bound competitively with Na" at the external transport site of the placental brush border Na /H exchanger, they concluded that the vicinal dithiol groups are necessary for transport function but are located at a site distinct from the external transport site. 

Taken together, these results indicate that similar to other proton-translocating membrane proteins, both types of Na /H exchangers contain critical sulfhydryl groups that are involved in the transport mechanism. These sulfhydryl groups do not appear to be present at the external transport site but may be involved in switching from an inactive to an activated state. 

GP 9] [R 16[ The extent of external transport limits was made in an approximate manner as for the internal transport limits (see above), as literature data on heat and mass transfer coefficients at low Peclet numbers are lacking [78]. Using a Pick s law analysis, negligible concentration differences from the bulk to the catalyst sur-... 

Figure 9. Effects of internal and external transport resistances on the computed step-response of CO adsorption. Curve A corresponds to our experimental conditions. Key A, km = 60 cm/s, Deff = 0.0246 cm2/s B, km —r oo, Detl = 0.246 cms/s and C, km — oo, Dell oo.

The activity calculated from (7) comprises both film and pore diffusion resistance, but also the positive effect of increased temperature of the catalyst particle due to the exothermic reaction. From the observed reaction rates and mass- and heat transfer coefficients, it is found that the effect of external transport restrictions on the reaction rate is less than 5% in both laboratory and industrial plants. Thus, Table 2 shows that smaller catalyst particles are more active due to less diffusion restriction in the porous particle. For the dilute S02 gas, this effect can be analyzed by an approximate model assuming 1st order reversible and isothermal reaction. In this case, the surface effectiveness factor is calculated from... 

For a more detailed analysis of measured transport restrictions and reaction kinetics, a more complex reactor simulation tool developed at Haldor Topsoe was used. The model used for sulphuric acid catalyst assumes plug flow and integrates differential mass and heat balances through the reactor length [16], The bulk effectiveness factor for the catalyst pellets is determined by solution of differential equations for catalytic reaction coupled with mass and heat transport through the porous catalyst pellet and with a film model for external transport restrictions. The model was used both for optimization of particle size and development of intrinsic rate expressions. Even more complex models including radial profiles or dynamic terms may also be used when appropriate. 

External transport resistance describes the rate of transport of the reactants from a bulk liquid phase through the stagnant liquid layer around the particles, which has to be overcome to reach the surface. The transport rate is commonly described by the equation... 

Zogorski et al. [125] indicate that external transport is the rate-limiting step in systems having poor mixing, dilute concentration of adsorbate, small particle sizes of adsorbent, and a high affinity of adsorbate for adsorbent. Some experiments conducted at low concentrations have shown that film diffusion solely controls the adsorption kinetics of low molecular weight substances [81,85]. 

The kinetic modeling of the external transport limitation is successful with aid of a double-substrate-limitation function [61-63] ... 

Diffusional effects were combined into apparent kinetic rate constants by using commercial-sized catalysts in kinetic experiments. The experiments were designed so that no significant external transport and axial dispersion effects occurred. 

When all the SE s of a solid with non-hydrostatic (deviatoric) stresses are immobile, no chemical potential of the solid exists, although transport between differently stressed surfaces takes place provided external transport paths are available. Attention should be given to crystals with immobile SE s which contain an (equilibrium) network of mobile dislocations. In these crystals, no bulk diffusion takes place although there may be gradients of the chemical free energy density and, in multicomponent systems, composition gradients (e.g., Cottrell atmospheres [A.H. Cottrell (1953)]). 

In an aqueous solution the ionic movement can be referred to the water molecules, which are unaffected by the applied electric field. But in a simple molten salt it is difficult to define the transport number because both ions are expected to move under the influence of the applied electric field. However, for a simple molten salt one can define an external transport number which is measured relative to a porous plug placed between the anode and cathode compartments of an electrolytic cell. Therefore, the ionic movement is related to a hypothetical exterior reference point of the molten salt. 

The Biot number Bim for mass transport. This can be interpreted as the ratio of internal to external transport resistance (intraparticle diffusion versus interphase diffusion) ... 

In the most general case, i.e. when intraparticlc and interphase transport processes have to be included in the analysis, the effectiveness factor depends on five dimensionless numbers, namely the Thiele modulus the Biot numbers for heat and mass transport Bih and Bim, the Prater number / , and the Arrhenius number y. Once external transport effects can be neglected, the number of parameters reduces to three, because the Biot numbers then approach infinity and can thus be discarded. 

Figure 6. Diagnostic tests for interphase (external) transport limitation.

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