Abstract
Electrophoresis is the motion of a charged colloidal particle in an electrolyte under an applied electric field. The electrophoretic velocity of a spherical particle depends on the dimensionless electric field strength
$\beta =a^*e^*E_\infty ^*/k_B^*T^*$
, defined as the ratio of the product of the applied electric field magnitude
$E_\infty ^*$
and particle radius
$a^*$
, to the thermal voltage
$k_B^*T^*/e^*$
, where
$k_B^*$
is Boltzmann's constant,
$T^*$
is the absolute temperature, and
$e^*$
is the charge on a proton. In this paper, we develop a spectral element algorithm to compute the electrophoretic velocity of a spherical, rigid, dielectric particle, of fixed dimensionless surface charge density
$\sigma$
over a wide range of
$\beta$
. Here,
$\sigma =(e^*a^*/\epsilon ^*k_B^*T^*)\sigma ^*$
, where
$\sigma ^*$
is the dimensional surface charge density, and
$\epsilon ^*$
is the permittivity of the electrolyte. For moderately charged particles (
$\sigma ={O}(1)$
), the electrophoretic velocity is linear in
$\beta$
when
$\beta \ll 1$
, and its dependence on the ratio of the Debye length (
$1/\kappa ^*$
) to particle radius (denoted by
$\delta =1/(\kappa ^*a^*)$
) agrees with Henry's formula. As
$\beta$
increases, the nonlinear contribution to the electrophoretic velocity becomes prominent, and the onset of this behaviour is
$\delta$
-dependent. For
$\beta \gg 1$
, the electrophoretic velocity again becomes linear in field strength, approaching the Hückel limit of electrophoresis in a dielectric medium, for all
$\delta$
. For highly charged particles (
$\sigma \gg 1$
) in the thin-Debye-layer limit (
$\delta \ll 1$
), our computations are in good agreement with recent experimental and asymptotic results.
Funder
Division of Chemical, Bioengineering, Environmental, and Transport Systems
Publisher
Cambridge University Press (CUP)
Subject
Mechanical Engineering,Mechanics of Materials,Condensed Matter Physics,Applied Mathematics
Cited by
2 articles.
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