Ion-exchange membranes solutions

Equality (1.20) is of primary importance because of the following reason. It is customary in most ionic transport theories to use the local electroneutrality (LEN) approximation, that is, to set formally e = 0 in (1.9c). This reduces the order of the system (1.9), (l.lld) and makes overdetermined the boundary value problems (b.v.p.s) which were well posed for (1.9). In particular, in terms of LEN approximation, the continuity of Ci and ip is not preserved at the interfaces of discontinuity of N, such as those at the ion-exchange membrane/solution contact or at the contact of two ion-exchange membranes or ion-exchangers, etc. Physically this amounts to replacing the thin internal (boundary) layers, associated with N discontinuities, by jumps. On the other hand, according to (1-20) at local equilibrium the electrochemical potential of a species remains continuous across the interface. (Discontinuity of Cj, ip follows from continuity of p2 and preservation of the LEN condition (1.13) on both sides of the interface.)... 

K. S. Spiegler, Polarization at ion exchange membrane-solution interfaces, Desalination, 9 (1971), pp. 367. 

Moya A A (2015) Theory of the formation of the electric double layer at the ion exchange membrane-solution interface. Phys Chem Chem Phys 17 5207-5218... 

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See also in sourсe #XX -- [ , , ]

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