Interdisciplinary Applied Mathematics

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7.5 Electrophoresis

Electrophoresis is the process of inducing motion of charged particles relative to a stationary liquid using an applied electric field, where the liquid acts as a conducting medium. The velocity at which charged parti-cles/molecules move toward the anode or cathode is known as the electrophoretic migration velocity. This motion is determined by a balance between the net particle charge under the EDL shielding and the opposing viscous drag. Therefore, electrophoretic migration velocity is proportional

to the    applied    electric field and    the    net    charge    of    the    particle,    and    it    is

inversely proportional to the viscosity of the liquid.

A particle in viscous fluid experiences strong hydrodynamic interactions. Assuming Stokes flow around a spherical particle of radius a, the velocity field    around    the    particle    decays    as (a/r),    r being    the    radial    distance

away from the particle. This gives very long interaction distances for parti-cle/particle and particle/fluid interactions; see Section 14.3.1. However, in electrophoretic motion, this interaction distance scales as (a/r)3, provided that the material properties, sizes, and zeta potentials of particles are the same, and the EDL thickness relative to the particle radius is very small (X/a ^ 1). (Reed and Morrison, 1976) studied hydrodynamic interactions in electrophoresis, and obtained analytical solutions for two spherical particle interactions. Here we summarize approximate results for two particles moving    along    and    normal    to    their line    of    centers.    In    the    first    case, the

electrophoretic mobility (pEP) is

where H is the center-to-center particle separation, and subscripts o and 1 identify the two particles. The electrophoretic mobility of two particles moving normal to their line of centers is

1- 7§(f)

i -H#)3

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