Migration of ion-exchange particles under the action of a uniformly applied<br/><br/>electric field

Tuesday, December 8, 2009 - 9:00am - 9:40am
EE/CS 3-180
Ehud Yariv (Technion-Israel Institute of Technology)
An ideally polarizable cation-selective solid particle is suspended in an
electrolyte solution and is exposed to a uniformly applied ambient electric
field. The electrokinetic transport processes are described in a closed
mathematical model, consisting of differential equations, representing the
physical balance laws, as well as boundary conditions and integral constraints,
representing the physicochemical condition on the particle boundary and at
distances away from it. Solving this model would in principle provide the
electro-kinetic flow about the particle and the concomitant particle drift
relative to the otherwise quiescent fluid.

Using matched asymptotic expansions, the model is analyzed in the
thin-Debye-layer limit. An effective `macroscale' description is extracted,
whereby effective boundary conditions represent appropriate asymptotic matching
with the Debye-scale fields. The macroscale description significantly differs
from that corresponding to a chemically inert ideally polarizable particle.
Thus, ion selectivity on the particle surface results in a macroscale salt
concentration polarization, whereby the electric potential is rendered
non-harmonic. Moreover, the uniform Dirichlet condition governing this
potential on the particle surface is transformed into a non-uniform Dirichlet
condition on the macroscale particle boundary. The Dukhin--Derjaguin slip
formula still holds, but with a non-uniform zeta potential that depends upon
the salt concentration distribution.

For weakly applied fields, an approximate solution is obtained as a
to an equilibrium state. The linearized solution corresponds to a uniform zeta
potential; it predicts a particle velocity which is proportional to the applied
field. The associated electrokinetic flow differs however from that in the
comparable electrophoresis of an inert particle surface, since it is driven by
two different agents, electric field and salinity gradients, which are of
comparable magnitude. The velocity field, specifically, is rotational.
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