Effective transport number

It must be pointed out that in a diffusion layer where the ions are transported not only by migration but also by diffusion, the effective transport numbers t of the ions (the ratios between partial currents ij and total current t) will differ from the parameter tj [defined by Eq. (1.13)], which is the transport number of ion j in the bulk electrolyte, where concentration gradients and diffusional transport of substances are absent. In fact, in our case the effective transport number of the reacting ions in the diffusion layer is unity and that of the nonreacting ions is zero. 

The ion transport number is defined as the fraction of current carried through the membrane by counterions. If the concentration of fixed charges in the membrane is high compared to the concentration of the ambient solution, then the mobile ions in the IX membrane are mosdy counterions, co-ions are effectively excluded, and the ion transport number then approaches 1. Commercial membranes have ion transport numbers in dilute solutions of ca 0.85—0.95. The relationship between ion transport number and current efficiency is shown in Figure 3 where is the fraction of current carried by the counterions (anions) through the AX membrane and is the fraction of current carried by the counterions (cations) through the CX membrane. The remainder of the current (1 — in the case of the AX membranes and (1 — in the case of the CX membranes is carried by co-ions and... 

In sodium chloride solutions the ion transport number for Na+ is about 0.4 compared to about 0.6 for CU. Thus a CX membrane would be expected to polarize at lower current densities than an AX membrane. Careful measurements show that CX membranes do polarize at lower current densities however, the effects on pH are not as significant as those found when AX membranes polarize. Such differences ia behavior have beea satisfactorily explaiaed as resultiag from catalysis of water dissociatioa by weaMy basic groups ia the AX membrane surfaces and/or by weaMy acidic organic compounds absorbed on such surfaces (5). 

Figure 13. Comparison between number average molecular weight predicted by axisymmetric model with effective transport properties and experimentally measured values for styrene [5] and vinyl acetate [2]. ...

AU these features—low values of a, a strong temperature dependence, and the effect of impurities—are reminiscent of the behavior of p- and n-type semiconductors. By analogy, we can consider these compounds as ionic semiconductors with intrinsic or impurity-type conduction. As a rule (although not always), ionic semiconductors have unipolar conduction, due to ions of one sign. Thus, in compounds AgBr, PbCl2, and others, the cation transport number is close to unity. In the mixed oxide ZrOj-nYjOj, pure 0 anion conduction t = 1) is observed. 

In porous separators the pore radii are large compared to the size of molecules. Hence, interaction between the electrolyte and the pore walls has practically no qualitative effects on the ionic current through the separator the transport numbers of the individuaf ions have the same vafues in the pores as in the bulk electrolyte, hi swollen membranes the specific interaction between individuaf ions and macromofecufes is very pronounced. Hence, these membranes often exhibit sefectivity in the sense that different ions are affected differentfy in their migration. As a resuft, the transport numbers of the ions in the membrane differ from those in the efectrofyte outside the membrane. In the limiting case, certain types of ion are arrested completely, and the membrane is called permselective (see Chapter 5). 

If measurements are made in thin oxide films (of thickness less than 5 nm), at highly polished Al, within a small acceptance angle (a < 5°), well-defined additional maxima and minima in excitation (PL) and emission (PL and EL) spectra appear.322 This structure has been explained as a result of interference between monochromatic electromagnetic waves passing directly through the oxide film and EM waves reflected from the Al surface. In a series of papers,318-320 this effect has been explored as a means for precise determination of anodic oxide film thickness (or growth rate), refractive index, porosity, mean range of electron avalanches, transport numbers, etc. 

A key factor in the possible applications of oxide ion conductors is that, for use as an electrolyte, their electronic transport number should be as low as possible. While the stabilised zirconias have an oxide ion transport number of unity in a wide range of atmospheres and oxygen partial pressures, the BijOj-based materials are easily reduced at low oxygen partial pressures. This leads to the generation of electrons, from the reaction 20 Oj + 4e, and hence to a significant electronic transport number. Thus, although BijOj-based materials are the best oxide ion conductors, they cannot be used as the solid electrolyte in, for example, fuel cell or sensor applications. Similar, but less marked, effects occur with ceria-based materials, due to the tendency of Ce ions to become reduced to Ce +. 

W. F. Graydon and R. J. Stewart (41) also compared the membrane potentials with the values according to equation (46). The membrane investigated was a copolymer of p-styrene sulfonic acid and styrene crosslinked with divinyl benzene. In the large majority of cases the experimental values were lower than those according to equation (46). The smaller part of this difference could be attributed to the transport of the co-ions and was calculated roughly. The greater part was attributed to water transport. From this the transport number of water was calculated it varied from 1 to about 60. It was found that the water transport was proportional to the water content and inversely proportional to the number of crosslinks. A provisional direct measurement was effected of a water transport number. The value corresponded rather well with the indirect determination as described above. 

Thus, any ED unit design or optimization exercise relies on quite a great number of engineering parameters, such as ion transport numbers in solution (t+ and t ) and electromembranes (t, ) effective solute (ts) and water (tw)... 

The effective solute (ts) transport number, ranged from 93% to 98%, even if reduced to 88% for sodium lactate. The water transport number (tw) increased from 9.3 to 15.6 and correspondently the maximum salt weight concentration in the concentrated stream (CBc,max) ranged from 286 to 350 kg/m3. Finally, while the surface resistance (rc) of the cation-exchange membranes was found to be about constant (5 2fl cm2), ra tended to increase with A/b. However, the specific electric energy consumption (e) slightly increased from 0.19 to 0.22 kWh/kg of salt recovered. 

Effect of the salt molecular mass (MB) on the cation transport number (C) in the corresponding solution effective solute (tB) and water (%) transport numbers surface resistances (rc, ra) of, and counterion transport numbers (tc+, ta ) in cation- and anion-exchange membranes specific electric energy consumption (e) in the case of 90% salt recovery at 1 A, and maximum solute concentration theoretically achievable in the concentrating stream (CBCmax). Note NaCl, sodium chloride Na-A, acetate Na-P, propionate Na-L, lactate. 

Obviously liquid residence time is not an appropriate parameter to describe pore diffusion effects in fluidized bed adsorption. This may be elucidated by assessing particle side transport by a dimensionless analysis. Hall et al. [73] described pore diffusion during adsorption by a dimensionless transport number Np according to Eq. (17), De denoting the effective pore diffusion coefficient in case of hindered transport in the adsorbent pores and Ue the... 

The limiting current density is determined by concentration-polarization effects at the membrane surface in the diluate containing compartment that in turn is determined by the diluate concentration, the compartment design, and the feed-flow velocity. Concentration polarization in electrodialysis is also the result of differences in the transport number of ions in the solution and in the membrane. The transport number of a counterion in an ion-exchange membrane is generally close to 1 and that of the co ion close to 0, while in the solution the transport numbers of anion and cations are not very different. 

The radiation-hydrodynamic simulation includes the Quotidien EOS [29] and Ion EOS based on the Cowan model [30], For the electron component, a set of fitting formulae derived from the numerical results from the Thomas-Fermi model and a semi-empirical bonding correction [31] are adopted. The effective Z-number of the partially ionized plasma is obtained from the average atom model. Radiation transport is treated by multigroup diffusion. 

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