Zhen Yuan
Anthony L. Garcia
Gabriel P. Lopez
Dimiter N. Petsev
Center for Biomedical
Engineering,
Department of Chemical and
Nuclear Engineering,
University of New Mexico,
Albuquerque, NM, USA
Received September 23, 2006
Revised November 17, 2006
Accepted November 23, 2006
Review
Electrokinetic transport and separations in
fluidic nanochannels
This article presents a summary of theory, experimental studies, and results for the elec-
trokinetic transport in small fluidic nanochannels. The main focus is on the effect of the
electric double layer on the EOF, electric current, and electrophoresis of charged analytes.
The double layer thickness can be of the same order as the width of the nanochannels,
which has an impact on the transport by shaping the fluid velocity profile, local distribu-
tions of the electrolytes, and charged analytes. Our theoretical consideration is limited to
continuum analysis where the equations of classical hydrodynamics and electrodynamics
still apply. We show that small channels may lead to qualitatively new effects like selective
ionic transport based on charge number as well as different modes for molecular separa-
tion. These new possibilities together with the rapid development of nanofabrication cap-
abilities lead to an extensive experimental effort to utilize nanochannels for a variety of
applications, which are also discussed and analyzed in this review.
Keywords:
Electric current conductivity / Electrokinetic transport / Electroosmosis / Nano-
fluidic channels DOI 10.1002/elps.200600612
Electrophoresis 2007, 28, 595–610 595
1 Introduction
The recent interest in fluidic nanochannels is constantly
increasing due to the wide range of applications that they
offer. Nanochannels have been used for chemical [1] and
biomolecular [2] sensing, separation of charged analytes [2–
7], and single DNA molecule manipulation [8–12]. These
applications were facilitated by the significant increase in the
range of advanced nanofabrication techniques. Nanochan-
nels are fabricated using bulk [13–19] and surface [1, 12, 20–
25] nanomachining, buried channel method [26], chemical–
mechanical polishing, and thermal oxidation [27]. Other
fabrication methods are based on electron beam [28] and
interferometric [29, 30] lithography or self-assembly pattern-
ing [31, 32].
The transport of fluid, electric current, and dissolved
analytes in very small channels of nanometer size presents
not only practical but also fundamental interest. At these
dimensions (a few tens to a few hundreds of nanometers) the
electric double layer that usually forms and the channel walls
become comparable in size to the channel width. The origin
of the charges at the surface is due to surface group dis-
sociation or adsorption of charged molecules from the solu-
tion. For example, silica surfaces acquire a charge when in
contact with an aqueous solution because of the dissociation
of the surface silanol groups. Silica is a common material for
nanochannel fabrication [30]. The typical electrokinetic

-potential of the silica–water interface is between 50 and
100 mV depending on the pH and the present electrolyte
[33]. The relative wall surface to channel bulk volume ratio
increases with decreasing the channel width and that facil-
itates a variety of adsorption effects. Hence, the fluid and the
dissolved molecular and ionic species in nanochannels are
subjected to stronger interactions with the walls. It is not
surprising that the transport phenomena in nanochannels
will have specific features that are not typical for larger
micrometer- and millimeter-sized channels and capillaries.
Large parts of the nanochannels could be occupied by the
electric double layers formed at the walls, and this fact has an
important impact on the fluid flow, electric current, and
transport of solutes, by shaping the fluid velocity profile and
spatial distribution of ions and charged analytes. A detailed
knowledge of these features allows for better optimization
and performance of the different practical applications.
We present an overview of the electrokinetic transport of
fluid, electric current, and dissolved analytes in small fluidic
nanochannels. The primary effects of interest stem from the
electric double layers that may propagate into the channel
interior. Our consideration is limited to continuum
approaches where the molecular structure of the fluid does
not need to be explicitly taken into account. The paper is
organized as follows: the next section discusses the available
Correspondence: Professor Dimiter N. Petsev, Department of
Chemical and Nuclear Engineering, 209 Farris Engineering Cen-
ter, University of New Mexico, Albuquerque, 87131, USA
E-mail: Dimiter@unm.edu
Fax: 1505-277-5433
Abbreviation: FET, field effect transistor
 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim www.proteomics-journal.de

596 Z. Yuan et al. Electrophoresis 2007, 28, 595–610
transport models. The electrostatic potential distribution in
the channel is the key quantity; hence, a brief analysis of the
Poisson–Boltzmann equation is also included. A special
attention is paid on the effect of the counterion charge and
the comparison between mono- and divalent ions. New pre-
dictions regarding the effect of the counterions on the trans-
port are presented. Section 3 is dedicated to the experimental
methods for studying the transport in nanochannels and
summarized some of the results they have produced. It
shows that reducing the size of the channel may result in
new modes of transport and separation of analytes. Section 4
summarizes the conclusions.
This article is dedicated to the memory of Dr. Andreas
Chrambach. During his career he performed pioneering
studies in the area of the fundamentals of gel electrophoresis
[34–37], and separation and analysis of proteins [38–40],
DNA [41–43], and subcellular particles [44–47]. Many of
these systems are now targets of the currently developing
fluidic nanochannel-based methods.
2 Theory of the electrokinetic transport in
nanochannels
List of symbols
A cross-section area of the channel
c
a
(r) local concentration of analyte
c
a
0
concentration of analyte in a large reservoir in flui-
dic contact with the channel
D
1
, D
2
diffusion coefficients of the background binary
electrolyte ions
E, E external electric field
e elementary charge
J
ep
analyte migration flux
J
eo
analyte convective flux
kT thermal energy (k is the Boltzmann constant, T is
the temperature in K7)
K
tot
total relative conductivity
K
tot
= K
ch
/K
b
; K
ch
is the channel conductivity, K
b
is
the conductivity in the bulk solution in thermo-
dynamic equilibrium with the double layer
n
i
the number (bulk) concentration of the ith ionic
species
U
eo
average bulk electroosmotic flow velocity
v
eo
electroosmotic fluid velocity
z
1
, z
2
co-ion and counterion charge numbers
z
a
charge number of the analyte
d thickness of the dielectric layer at the channel wall
e relative dielectric permittivity
e
0
dielectric constant of vacuum
e
d
relative permittivity of the material of the channel
wall
Z solvent viscosity
k inverse thickness of the electrical double layer
r
e
charge density
s the surface charge
z electrokinetic zeta potential of the channel wall
z
a
electrokinetic potential of the analyte
e
z dimensionless electrokinetic potential
e
z = ez=kT
C electrostatic potential
e
C dimensionless electrostatic potential
e
C ¼ eC=kT
C
1
the potential of a single double layer
The transport of fluid, current, and dissolved molecules in
small fluidic nanochannels is affected by the close proximity
of the wall surfaces. The channel walls usually acquire a
charge when in contact with most fluids of interest like
various aqueous solutions. Hence, the transport is governed
by electrokinetic phenomena, which depend on the electro-
static potential distribution in the channel [48–51]. Figure 1
illustrates the distribution of charges at a solid–liquid inter-
face (single double layer). The solid in the picture is nega-
tively charged, but this is not necessarily the case for all the
systems. The ion redistribution in the vicinity of the inter-
face leads to a local charge density, which in turn leads to
the motion of the fluid (electroosmosis) or the solid (elec-
trophoresis) if external field is applied. Electrokinetic phe-
nomena like electroosmosis and electrophoresis are used to
drive fluids and analytes in small channels while the elec-
troviscosity determines the hydrodynamic resistance for
pressure-driven flow. Knowing the potential distribution is
necessary for modeling and optimization of the transport in
fluidic devices. The electrostatic potential magnitude is
characterized by the electrokinetic
-potential defined at the
plane of fluid shear near the channel wall or the surface of a
moving particle (see Fig. 1a) [48–50]. The range of the elec-
trostatic potential is usually estimated by the so-called dou-
ble layer thickness, which indicates the rate of potential
decay with distance [52–55]. This thickness depends on the
ionic strength of the solution and decreases with the
increase in the electrolyte concentration. Thus, monovalent
electrolyte concentrations between 10
26
and 10
22
M lead to
double layer thicknesses ranging from 300 to 3 nm. Regular
CE and most microfluidic devices have channels that are
much greater than the double layer thickness developed
inside the solutions. This fact allows for significant simpli-
fication in the theoretical analysis [48, 49] and easy data
interpretation. In the case of fluidic nanochannels, however,
the situation could be very different because typically the
nanochannel width (or diameter) could be of the same order
as the double layer thickness determined by the ionic
strength of the flowing solution. In the present section, we
consider the case where the electric double layer formed at
 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim www.proteomics-journal.de