Combined migration—diffusion

The mobility, u, of an ion expresses the ease with which it responds to a gradient of electric potential. The diffusion coefficient, D, of an ion expresses the ease with which it responds to a gradient of its concentration. One might well imagine that a relationship exists between u and D. This is indeed the case the relation is 

The mobility u and diffusion coefficient D of an ion are two of the trio of transport parameters of which the third is the equivalent ionic conductivity X. Conductivity is not a topic here and we will merely quote the 

Among the uses of these relations is their value in providing estimates of the diffusion coefficient of an ion (but watch the units ). 

We have ruled out convection, but must still treat situations in which transport occurs by the two remaining modes. In such cases, the total flux of an ion contains a migratory contribution and a diffusive contribution. Hence using eqns. (21) and (23) 

Making use of the Nemst—Einstein equation, expression (33) can be rewritten for the combined migration—diffusion flux as 

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Transport by combined migration—diffusion in a finite planar geometry can achieve a true steady state when only two ions are present, as we saw in Sect. 4.2. The same holds true when there are three or more ions present. Under simplifying conditions [see eqn. (89) below], it is possible to predict the steady-state behaviour with arbitrary concentrations of many ions. However, the corresponding transient problem is much more difficult and we shall not attempt to derive the general transient relationship, as we were able to do in deriving eqn. (82) in the two-ion case. 

Ions can be transported through an electrochemical solution by three mechanisms. These are migration, diffusion, and convection. Electroneutrality must be maintained. The movement of ions in a solution gives rise to the flow of charge, or an ionic current. Migration is the movement of ions under the influence of an electric field. Diffusion is the movement of ions as driven by a concentration gradient, and convection is the movement due to fluid flow. In combination these terms produce differential equations with nonlinear boundary conditions (1). 

At steady state, the production rate of metal ions by dissolution is equal to the combined migration and diffusion removing metal ions from the crevice. Of course, there is no source of anions such as chloride within the occluded region, so that at steady state, the removal of chloride ions by diffusion is equally balanced by its ingress due to migration as shown in Fig. 12. 

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Cross-flow-elec trofiltratiou (CF-EF) is the multifunctional separation process which combines the electrophoretic migration present in elec trofiltration with the particle diffusion and radial-migration forces present in cross-flow filtration (CFF) (microfiltration includes cross-flow filtration as one mode of operation in Membrane Separation Processes which appears later in this section) in order to reduce further the formation of filter cake. Cross-flow-electrofiltratiou can even eliminate the formation of filter cake entirely. This process should find application in the filtration of suspensions when there are charged particles as well as a relatively low conduc tivity in the continuous phase. Low conductivity in the continuous phase is necessary in order to minimize the amount of elec trical power necessaiy to sustain the elec tric field. Low-ionic-strength aqueous media and nonaqueous suspending media fulfill this requirement. 

Trai brt. of Ions . the, combined mottoh. of ions in an electrOIyte, (solid Or liquid) under, diffusion and migration. ... 

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