Microgravity Sci. Technol. (2010) 22:329–338
DOI 10.1007/s12217-010-9195-8
ORIGINAL ARTICLE
The Effect of Axial Concentration Gradient
on Electrophoretic Motion of a Charged
Spherical Particle in a Nanopore
Sang Yoon Lee · Sinan E. Yalcin · Sang W. Joo ·
Ashutosh Sharma · Oktay Baysal · Shizhi Qian
Received: 30 November 2009 / Accepted: 3 April 2010 / Published online: 24 April 2010
© Springer Science+Business Media B.V. 2010
Abstract The electrophoretic motion of a charged
spherical nanoparticle along the axis of a nanopore
connecting two fluid reservoirs, subjected to an axial
electric field and electrolyte concentration gradient, has
been investigated using a continuum model. The model
consists of the Poisson and Nernst–Planck equations for
the electric potential and ionic concentrations and the
Stokes equations for the hydrodynamic field with zero
gravity. In addition to the electrophoresis generated
by the externally imposed electric field, the particle
also experiences diffusiophoresis arising from the ex-
ternally imposed concentration gradient. The effects of
the diffusiophoresis on the axial electrophoretic motion
are examined with changes in the ratio of the particle
size to the thickness of the electric double layer (EDL),
and the imposed concentration gradient. Since the EDL
thickness, the particle size, and the nanopore size are
of the same order of magnitude, the diffusiophoresis
is dominated by the induced electrophoresis driven by
the generated electric field arising from the double-
layer polarization (DLP). For a relatively small κap,
the ratio of the particle size to the EDL thickness,
the diffusiophoresis is dominated by the induced elec-
S. Y. Lee · S. W. Joo · A. Sharma · S. Qian
School of Mechanical Engineering, Yeungnam University,
Gyongsan 712-749, South Korea
S. E. Yalcin · O. Baysal · S. Qian (B)
Department of Aerospace Engineering,
Old Dominion University, Norfolk, VA 23529, USA
e-mail: sqian@odu.edu
A. Sharma
Department of Chemical Engineering,
Indian Institute of Technology, Kanpur 208016, India
trophoresis from the type II DLP, which propels the
particle toward regions with lower salt concentration.
Depending on the magnitude and direction of the
externally imposed concentration gradient, the elec-
trophoretic motion can be accelerated, decelerated, and
even reversed by the diffusiophoresis.
Keywords Electrophoresis · Diffusiophoresis ·
Electrical double layer · Nanopore
Introduction
In recent years, there has been a growing interest in
developing nanopore-based nanofluidic devices with
features comparable in size to DNA, proteins and
other biological molecules for biological and chemi-
cal analysis (Branton et al. 2008; Lemay 2009; Clarke
et al. 2009). In nanofluidic devices, it is necessary to
manipulate fluids or nanoparticles such as DNA for
various applications. Since the sample volume is ex-
tremely small, the gravitational body force is negligible.
The interfacial electrokinetic phenomena such as elec-
troosmosis and electrophoresis are thus widely used
to manipulate fluids and/or particles in microfluidic
and nanofluidic applications (Li 2004; Masliyah and
Bhattacharjee 2006; Branton et al. 2008; Lemay 2009;
Clarke et al. 2009; Ai et al. 2009a, b, 2010a, b).
When a charged particle is immersed in an elec-
trolyte solution, the accumulation of a net electric
charge near its surface leads to the formation of an
EDL. In the presence of an external electric field,
both the charges on the particle and the ions in the
EDL interact with the overall electric field near the
particle, resulting in electrostatic forces acting on both

330 Microgravity Sci. Technol. (2010) 22:329–338
the particle and the fluid and resulting in simultaneous
electrophoretic and electroosmotic motions. The elec-
trophoresis of charged and non-charged particles that
acquire charge by polarization has been widely utilized
in characterizing, separating, and purifying colloidal
particles and macromolecules, such as DNA fragments,
proteins, drugs, viruses, and biological cells (Li 2004).
For example, when a DNA molecule is electrophoret-
ically driven through a nanopore, nucleobases would
modify the ionic current through the nanopore, and
thus the sequence of bases in DNA might be recorded
by monitoring the current modulations (Branton et al.
2008; Lemay 2009; Clarke et al. 2009). This nanopore-
based DNA sequencing method is called the third gen-
eration DNA sequencing, and its cost is believed to be
sufficiently low. Therefore, this new technology might
potentially revolutionize genomic medicine (Branton
et al. 2008; Clarke et al. 2009).
In the existing study on nanoparticle translocation
through a nanopore, the particle motion is driven by
the externally imposed electric field, while the elec-
trolyte concentrations in the two fluid reservoirs are the
same. In the present study, electrophoretic motion of
a charged nanoparticle in a nanopore connecting two
fluid reservoirs filled with different electrolyte concen-
trations is studied for the first time. Since the elec-
trolyte concentrations on both sides of the nanopore
are different, diffusiophoretic motion is also induced in
addition to the electrophoresis (Anderson and Prieve
1984; Keh and Li 2007; Qian et al. 2007; Lou and Lee
2008a, b; Keh and Wan 2008; Abecassis et al. 2008,
2009; Prieve 2008; Lou et al. 2009; Hsu et al. 2009, 2010;
Hsu and Keh 2009; Zhang et al. 2009). Depending on
the magnitude and direction of the imposed concen-
tration gradient, the induced diffusiophoretic motion
can enhance the particle’s electrophoretic motion or
slow down nanoparticle translocation in a nanopore,
and thus can be used to regulate the nanoparticles
translocation process to achieve a nanometer-scale spa-
tial accuracy for DNA sequencing. In particular, it is
conceivable that slowing down the motion of DNA in a
nanopore by diffusiophoretic control seems especially
attractive as it would offer a greater window of oppor-
tunity for enhanced spatio-temporal resolution.
In the following section, a “Mathematical Model” is
introduced based on the continuum hypothesis for the
fluid motion and the ionic mass transport. The former
is induced by the externally imposed electric field and
concentration gradient and the latter accounts for the
polarization of the EDL and is valid for any thickness
of the EDL. The effect of the imposed concentration
gradient on the electrophoretic motion of a nanoparti-
cle along the axis of a nanopore is presented in “Results
and Discussion”, followed by concluding remarks in
“Conclusions”.
Mathematical Model
We consider an uncharged nanopore of length L and
radius a connecting two identical reservoirs, as shown
in Fig. 1. An axisymmetric cylindrical coordinate sys-
tem (r, z) with the origin located at the center of the
nanopore is used. A charged spherical nanoparticle of
radius ap and surface charge density σp is submerged
in an electrolyte solution in the nanopore. We assume
that the nanoparticle is initially positioned with axis
coinciding with the nanopore’s axis, and the location of
the particle’s center of mass coincides with the origin.
The axisymmetrical model geometry is represented by
the region bounded by the outer boundary ABCDE-
FGH, the line of symmetry HI, the particle’s surfaces
IJ and JK, and the symmetry line KA. The dashed
line segments, AB, BC, FG, and GH represent the
regions in the reservoirs. The lengths LR and radius
b of the reservoirs are sufficiently large to ensure that
the electrochemical properties at the locations of AB,
BC, FG and GH are not influenced by the charged
Fig. 1 Schematic of a
nanopore of length L and
radius a connecting two
identical reservoirs on either
side. A concentration
gradient of electrolyte
solution and an electric field
are applied across the two
reservoirs. A charged
spherical particle of radius ap
bearing uniform surface
charge density, σp, is
positioned at the center of the
nanopore