# Mobility paradox

Dear colleges on the Computational Chemistry List,
this morning I thought about an apparently simple problem where I do not
know a solution jet. Consider a symmetric 1:1 electrolyte system with a
single dielectric constant which is divided by a planar surface into a
right hand and a left hand side. The cationic and anionic concentrations,
cC and cA, on both sides are the same; to obtain global electro neutrality
cC == cA is required. Exceptions from this rule are allowed only locally,
e.g. within a few Debye length around the boundary. The ionic mobilities
are mu1 > mu2 on the right hand side and mu2 and mu1 on the other for
cations and anions, respectively. At equilibrium there is no problem.
Now an external electric field E is applied and this creates the problem.
On the first view one would write the individual ionic fluxes jC and jA far
away from the central boundary:
left hand side and right hand side
cations jC(left) = + F mu1 E cC and jC(right) = + F mu2 E cC
anions jA(left) = - F mu2 E cA and jA(right) = - F mu1 E cA
where F is Faraday's constant. But this implies jC(left) != jC(right) and
jA(left) != jA(right) which violates the particle conservation law. I would
assume that such a problem has been discussed in literature. Has anybody
some ideas?
I will summarize the replies.
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Eberhard von Kitzing
Max-Planck-Institut fuer Medizinische Forschung
Jahnstr. 29, D69120 Heidelberg, FRG
Carl-Zuckmayer Str. 17, D69126 Heidelberg (privat)
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Tel.: +49-6221-486 467 (work)
Tel.: +49-6221-385 129 (home)
internet: vkitzing-: at :-sunny.MPImF-Heidelberg.mpg.de
http://sunny.mpimf-heidelberg.mpg.de/people/vkitzing/Eberhard.html