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.
 -------------------------------------------------------------------------
 Eberhard von Kitzing
 Max-Planck-Institut fuer Medizinische Forschung
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 http://sunny.mpimf-heidelberg.mpg.de/people/vkitzing/Eberhard.html