Interdisciplinary Applied Mathematics

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These approximate relations are valid for large separation distances, and uEP and E vectors are in the same direction. The terms in the denominator are corrections due to the electric field in the presence of particles, and the numerator terms are due to the particle/particle interactions. A striking outcome of these approximate results (equally valid for the analytical/exact results) is that there are no particle/particle interactions if the particle size and zeta potential are the same. For particle size or zeta potential mismatch, the interactions decay like (a/d)3. These conditions enable a similarity between the electric field and the velocity field, so that the flow outside the EDL region obeys potential flow conditions, which also satisfy the Stokes equations. Implications of this result are quite important:

Electrophoretic particle motion does not disturb the surrounding fluid to a great extent (Reed and Morrison, 1976).

Therefore, one can model the steady particle motion using a simple mobility concept, where the particle velocity can be found by

UEP — PepE.

The reader is referred to (Swaminathan and Hu, 2004), for results on particle interactions in electrophoresis due to inertial effects.

The mobility concept can also be applied to a large number of particles and dilute species. Reed and Morrison (1976) compared their findings with several experimental results. They reported that for the thin EDL cases, mobilities of groups of particles remain constant for a wide range of particle concentrations. In the following section, we will review the governing equations for charged species transport and present experimental results and numerical modeling efforts for electrophoresis using the aforementioned mobility concept.

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