Migration mass transfer

Electrochemistry constitutes an important discipline that involves many phenomena as mass transfer, migration because of the presence of electric field, and hydrodynamic especially in reactor with large scale. 

Electrodialysis. In reverse osmosis pressure achieves the mass transfer. In electro dialysis (qv), dc is appHed to a series of alternating cationic and anionic membranes. Anions pass through the anion-permeable membranes but are prevented from migrating by the cationic permeable membranes. Only ionic species are separated by this method, whereas reverse osmosis can deal with nonionic species. The advantages and disadvantages of reverse osmosis are shared by electro dialysis. 

When reactants are distributed between several phases, migration between phases ordinarily will occur with gas/liquid, from the gas to the liquid] with fluid/sohd, from the fluid to the solid between hquids, possibly both ways because reactions can occur in either or both phases. The case of interest is at steady state, where the rate of mass transfer equals the rate of reaction in the destined phase. Take a hyperbohc rate equation for the reaction on a surface. Then,... 

For electrolytic solutions, migration of charged species in an electric field constitutes an additional mechanism of mass transfer. Thus the flux of an ionic species Nj in (g mol)/(cm s) in dilute solutions can be expressed as... 

To consider the convective mass transfer problem of a rotating hemisphere electrode, we assume that sufficient inert salts are present in the electrolyte that the migrational... 

In binary solutions, for example, CuS04 in H20, the limiting current exceeds that due to convective diffusion alone by a factor of about two. The excess mass transfer is caused by migration of the reacting ion in the electric field. In both forced and free convection it is important to know the ion flux contributed by migration, which can never be suppressed completely. 

Migration of the reacting ion in the electric field, briefly referred to in Section II,B, is usually suppressed by the addition of excess inert electrolyte. Incorrect values for mass-transfer rates are obtained if migration contributes more than a negligible fraction of the total limiting current. 

The diffusivities thus obtained are necessarily effective diffusivities since (1) they reflect a migration contribution that is not always negligible and (2) they contain the effect of variable properties in the diffusion layer that are neglected in the well-known solutions to constant-property equations. It has been shown, however, that the limiting current at a rotating disk in the laminar range is still proportional to the square root of the rotation rate if the variation of physical properties in the diffusion layer is accounted for (D3e, H8). Similar invariant relationships hold for the laminar diffusion layer at a flat plate in forced convection (D4), in which case the mass-transfer rate is proportional to the square root of velocity, and in free convection at a vertical plate (Dl), where it is proportional to the three-fourths power of plate height. 

Here we also consider sorption kinetics as the mass-transfer barrier to surfactant migration to and from the interface, and we follow the Levich framework. However, our analysis does not confine all surface-tension gradients to the constant thickness film. Rather, we treat the bubble shape and the surfactant distribution along the interface in a consistent fashion. 

Figure 15.2E shows the effect of stationary phase mass transfer. After molecules of sample diffuse into a pore, they migrate to the stationary phase (shaded region) or become attached to it in some fashion. If a molecule penetrates deep into the stationary phase, it spends a longer time in the particle and travels a shorter distance down the column, just as in Fig. 15.2D. Molecules that spend only a little time moving into and out of the stationary phase return to the mobile phase sooner, and move further down the column.

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