Sample Preconcentration in Nanochannels with Nonuniform Surface
Charge and Thick Electric Double Layers
A. Eden*1
, C. McCallum1, B. Storey
2, S. Pennathur
1, C. D. Meinhart
1
1University of California, Santa Barbara,
2Olin College
*Corresponding author: Department of Mechanical Engineering, University of California, Santa Barbara, Santa
Barbara, CA 93106-5070. Email: [email protected]
Abstract: We present a novel method for
concentrating and focusing small analytes by
taking advantage of the nonuniform ion
distributions produced by thick electric double
layers (EDLs) in nanochannels with
heterogeneous surface charge. Specifically, we
apply a voltage bias to gate electrodes embedded
within the channel walls, tuning the surface
charge in a region of the channel and
subsequently altering the ionic strength and
charge density in that region relative to the rest
of the channel. The resulting nonuniform
electromigration fluxes in the different regions
serve to stack charged sample ions near an
interface where a step change in zeta potential
occurs, providing enhancement ratios superior to
those exhibited in traditional microchannel field
amplified sample stacking (FASS). Numerical
simulations are performed to demonstrate the
phenomenon, and resulting velocity and salt
concentration profiles show good agreement with
analytical results.
Keywords: nanofluidics, electrokinetic
preconcentration, electroosmosis, electrophoresis
1. Introduction
Recent advances in micro- and nanoscale
fabrication technologies have spurred the
development of myriad novel devices for
bioassays, DNA separation/amplification, and
other lab-on-chip processes [1-6]. However, the
small size scale of these devices introduces
several obstacles that must be overcome through
engineering prowess. A primary concern remains
the necessity for sample analyte preconcentration
in bioanalytical micro and nanofluidic devices
[7,8]. Many innovative focusing techniques
utilizing electrokinetic phenomena such as
FASS, ion concentration polarization,
isotachophoresis, isoelectric focusing, and
concentration gradient focusing have been
introduced in previous works to address and
attempt to resolve this prevalent issue in on-chip
applications [1-11]. Devices employing these
mechanisms often exploit the competition
between electroosmotic flow (EOF) and
electrophoresis in micro- and nanofluidic
systems in order to create regions of localized
ion enrichment. These enriched ions can then be
used for further downstream processing once the
level of sample molecules reaches the threshold
limit detectable by modern sensing capabilities.
Traditional microfluidic FASS involves the
injection of a low concentration sample plug
solution into a channel in order to create a
conductivity gradient between the plug and the
bulk fluid. These conductivity gradients produce
electric field gradients which drive sample ions
to “stack” at an equilibrium position where the
various forces balance. Bharadwaj and Santiago
comprehensively summarized the driving forces
behind the stacking mechanism in microchannels
[8], while Sustarich et al presented new findings
of increased sample enhancement in the
nanoscale regime due to pressure gradient
induced flow focusing and electrostatic repulsion
from finite-sized electric double layers (EDLs)
relative to the channel height [9].
We extend these works by investigating the
effects of thick, overlapped EDLs on the
behavior of background electrolyte ions and
sample ions in a nanochannel with nonuniform
EOF. Other authors have previously investigated
the effects of nonuniform EOF realized through
means ranging from field effect control to EOF
suppressing surface treatments [12-14]. Such
channels have been shown to exhibit tremendous
promise when it comes to controlling the
behavior of bulk fluid and individual ions in
applications such as nanofluidic diodes and field
effect transistors [15-17].
Further, we have found that it is theoretically
possible to create regions of nonuniform
conductivity and electric fields within a single
buffer solution by simply tailoring the surface
charge in select regions of a nanochannel. We
have therefore designed a tunable nanofluidic
preconcentration system with embedded gate
electrodes, allowing for field effect control of
Excerpt from the Proceedings of the 2016 COMSOL Conference in Boston
Figure 1:
in the channel with
embedded electrode (bottom right).
surface charge heterogeneity on the top and
bottom channel walls with the application of a
gate voltage
generate nonuniform EOF and regions of
controllable electrophoretic sample motion
within the channel. Our technique is
demonstrated with 2D numerical simulations
using COMSOL Multiphysics finite element
software. The numeri
ion distributions in fully developed regions of
the flow compare favorably with results from 1D
analytical models for both thick and thin EDL
cases. The parti
sample enhancement are shown to only occ
channels with sufficiently large
layers relative to the channel height, and in
channels with nonuniform surface charge.
Sample
simulations
The unique characteristics o
interactions in
thick EDLs suggest
investigation and optimization
2. Theory
2.1 Electric Double Layer
When aqueous electrolyte solutions come
into contact with a
chemical interactions often leave the surface
with a net charge. Free ions in solution are
subsequently attracted to the charged surface,
forming an electric double layer of ions. In the
first layer adjacent to the wall, often referr
as the Stern Layer, a thin layer of oppositely
charged
attracted to the charged surface
they are essentially adsorbed on
Figure 1: Diagram of the device with embedded electrodes (bottom left), with insets showing example ion distributions
in the channel with a slightly
embedded electrode (bottom right).
surface charge heterogeneity on the top and
bottom channel walls with the application of a
gate voltage (see Figure
generate nonuniform EOF and regions of
controllable electrophoretic sample motion
within the channel. Our technique is
demonstrated with 2D numerical simulations
using COMSOL Multiphysics finite element
software. The numeri
ion distributions in fully developed regions of
the flow compare favorably with results from 1D
analytical models for both thick and thin EDL
cases. The particular mechanisms which cause
sample enhancement are shown to only occ
channels with sufficiently large
layers relative to the channel height, and in
channels with nonuniform surface charge.
Sample enhancement ratios
simulations exceed those from traditional FASS
unique characteristics o
interactions in nano
thick EDLs suggest
investigation and optimization
Theory
2.1 Electric Double Layer
When aqueous electrolyte solutions come
into contact with a
chemical interactions often leave the surface
with a net charge. Free ions in solution are
subsequently attracted to the charged surface,
forming an electric double layer of ions. In the
first layer adjacent to the wall, often referr
as the Stern Layer, a thin layer of oppositely
charged counter-ion
attracted to the charged surface
ey are essentially adsorbed on
Diagram of the device with embedded electrodes (bottom left), with insets showing example ion distributions
slightly modified surface charge (top center) and the EDL potential and velocity profiles near an
embedded electrode (bottom right).
surface charge heterogeneity on the top and
bottom channel walls with the application of a
(see Figure 1). This is used to
generate nonuniform EOF and regions of
controllable electrophoretic sample motion
within the channel. Our technique is
demonstrated with 2D numerical simulations
using COMSOL Multiphysics finite element
software. The numerical velocity, potential, and
ion distributions in fully developed regions of
the flow compare favorably with results from 1D
analytical models for both thick and thin EDL
cular mechanisms which cause
sample enhancement are shown to only occ
channels with sufficiently large electric double
layers relative to the channel height, and in
channels with nonuniform surface charge.
enhancement ratios from our
exceed those from traditional FASS
unique characteristics of the
nanochannels with nonuniform
thick EDLs suggest that there is room for further
investigation and optimization of this process
2.1 Electric Double Layer
When aqueous electrolyte solutions come
into contact with a solid surface
chemical interactions often leave the surface
with a net charge. Free ions in solution are
subsequently attracted to the charged surface,
forming an electric double layer of ions. In the
first layer adjacent to the wall, often referr
as the Stern Layer, a thin layer of oppositely
ions are electrostatically
attracted to the charged surface so strongly
ey are essentially adsorbed on
Diagram of the device with embedded electrodes (bottom left), with insets showing example ion distributions
modified surface charge (top center) and the EDL potential and velocity profiles near an
surface charge heterogeneity on the top and
bottom channel walls with the application of a
). This is used to
generate nonuniform EOF and regions of
controllable electrophoretic sample motion
within the channel. Our technique is
demonstrated with 2D numerical simulations
using COMSOL Multiphysics finite element
cal velocity, potential, and
ion distributions in fully developed regions of
the flow compare favorably with results from 1D
analytical models for both thick and thin EDL
cular mechanisms which cause
sample enhancement are shown to only occur in
electric double
layers relative to the channel height, and in
channels with nonuniform surface charge.
from our 2D
exceed those from traditional FASS.
f the ion-EDL
channels with nonuniform,
there is room for further
of this process.
When aqueous electrolyte solutions come
surface, various
chemical interactions often leave the surface
with a net charge. Free ions in solution are
subsequently attracted to the charged surface,
forming an electric double layer of ions. In the
first layer adjacent to the wall, often referred to
as the Stern Layer, a thin layer of oppositely
s are electrostatically
so strongly that
ey are essentially adsorbed on the surface.
Diagram of the device with embedded electrodes (bottom left), with insets showing example ion distributions
modified surface charge (top center) and the EDL potential and velocity profiles near an
surface charge heterogeneity on the top and
bottom channel walls with the application of a
). This is used to
generate nonuniform EOF and regions of
controllable electrophoretic sample motion
within the channel. Our technique is
demonstrated with 2D numerical simulations
using COMSOL Multiphysics finite element
cal velocity, potential, and
ion distributions in fully developed regions of
the flow compare favorably with results from 1D
analytical models for both thick and thin EDL
cular mechanisms which cause
ur in
electric double
layers relative to the channel height, and in
channels with nonuniform surface charge.
2D
.
EDL
,
there is room for further
When aqueous electrolyte solutions come
, various
chemical interactions often leave the surface
with a net charge. Free ions in solution are
subsequently attracted to the charged surface,
forming an electric double layer of ions. In the
ed to
as the Stern Layer, a thin layer of oppositely
s are electrostatically
that
the surface.
Slightly farther away from the wall is a second
layer of
surface but are free to move due to diffusive
effects. Outside this diffuse layer, the ions in the
bulk solution are shielded from the charged
surface by the presence of the ions in the EDL.
When an external
ions
lines.
of the fluid within the EDL
along with it, generating an electroosmotic flow
profile.
The resulting distribution of ion
near the charged surface
potential
the wall
bulk fluid
potential distribution
related to the spatial free charge densi
in solution using
where
the
solution, and
density. The charge density effectively
represents the net charge present due to a local
imbalance of cations and anions in solution,
which for
as KCl
where
concentration of cations, and
concentration of anions
statistics to account for the relative energy
content of the ions in so
ions near a charged surface is approximated as
an exponentially decaying function
Diagram of the device with embedded electrodes (bottom left), with insets showing example ion distributions
modified surface charge (top center) and the EDL potential and velocity profiles near an
Slightly farther away from the wall is a second
layer of counter-ions that are still attracted to the
surface but are free to move due to diffusive
effects. Outside this diffuse layer, the ions in the
bulk solution are shielded from the charged
surface by the presence of the ions in the EDL.
When an external
ions within the EDL
. The resulting shear stress
of the fluid within the EDL
along with it, generating an electroosmotic flow
profile.
The resulting distribution of ion
near the charged surface
potential profile which is largest in m
the wall zeta potential
bulk fluid for large channels
potential distribution
related to the spatial free charge densi
in solution using Poisson
��
where�� is the permittivity of free space,
the relative permittivity of the electrolyte
solution, and �� is the local volumetric charge
density. The charge density effectively
represents the net charge present due to a local
imbalance of cations and anions in solution,
which for a binary monovalent electrolyte
as KCl can be expressed as
where � is Faraday’s constant,
concentration of cations, and
concentration of anions
statistics to account for the relative energy
content of the ions in so
ions near a charged surface is approximated as
exponentially decaying function
� �
Diagram of the device with embedded electrodes (bottom left), with insets showing example ion distributions
modified surface charge (top center) and the EDL potential and velocity profiles near an
Slightly farther away from the wall is a second
ions that are still attracted to the
surface but are free to move due to diffusive
effects. Outside this diffuse layer, the ions in the
bulk solution are shielded from the charged
surface by the presence of the ions in the EDL.
When an external electric field is applied, the
within the EDL will migrate
he resulting shear stress from the motion
of the fluid within the EDL pulls the bulk flu
along with it, generating an electroosmotic flow
The resulting distribution of ion
near the charged surface gives rise to an electric
which is largest in m
zeta potential ζ and decays to zero in the
for large channels. This transverse
potential distribution Ψ in the EDL can be
related to the spatial free charge densi
Poisson’s equation,
��� ��Ψ ��, is the permittivity of free space,
permittivity of the electrolyte
is the local volumetric charge
density. The charge density effectively
represents the net charge present due to a local
imbalance of cations and anions in solution,
binary monovalent electrolyte
can be expressed as ��is Faraday’s constant,
concentration of cations, and �concentration of anions. Using Boltzmann
statistics to account for the relative energy
content of the ions in solution, the distribution of
ions near a charged surface is approximated as
exponentially decaying function
,� exp �������� �
Diagram of the device with embedded electrodes (bottom left), with insets showing example ion distributions
modified surface charge (top center) and the EDL potential and velocity profiles near an
Slightly farther away from the wall is a second
ions that are still attracted to the
surface but are free to move due to diffusive
effects. Outside this diffuse layer, the ions in the
bulk solution are shielded from the charged
surface by the presence of the ions in the EDL.
ield is applied, the
migrate along field
from the motion
pulls the bulk fluid
along with it, generating an electroosmotic flow
The resulting distribution of ions in the EDL
gives rise to an electric
which is largest in magnitude at
and decays to zero in the
. This transverse
in the EDL can be
related to the spatial free charge density of ions
equation,
(1
is the permittivity of free space, � permittivity of the electrolyte
is the local volumetric charge
density. The charge density effectively
represents the net charge present due to a local
imbalance of cations and anions in solution,
binary monovalent electrolyte such
� ���� � ��is Faraday’s constant, �� is the molar �� is the molar
. Using Boltzmann
statistics to account for the relative energy
lution, the distribution of
ions near a charged surface is approximated as
exponentially decaying function
�, (2
Diagram of the device with embedded electrodes (bottom left), with insets showing example ion distributions
modified surface charge (top center) and the EDL potential and velocity profiles near an
Slightly farther away from the wall is a second
ions that are still attracted to the
surface but are free to move due to diffusive
effects. Outside this diffuse layer, the ions in the
bulk solution are shielded from the charged
surface by the presence of the ions in the EDL.
ield is applied, the
along field
from the motion
id
along with it, generating an electroosmotic flow
s in the EDL
gives rise to an electric
agnitude at
and decays to zero in the
. This transverse
in the EDL can be
ty of ions
1)
is
permittivity of the electrolyte
is the local volumetric charge
density. The charge density effectively
represents the net charge present due to a local
imbalance of cations and anions in solution,
such
��, is the molar
e molar
. Using Boltzmann
statistics to account for the relative energy
lution, the distribution of
ions near a charged surface is approximated as
2)
Excerpt from the Proceedings of the 2016 COMSOL Conference in Boston
where � is the ion valence, �� is the elementary
charge, ��� represents the thermal energy, and �,� is the bulk concentration of cations and
anions sufficiently far from the surface. The
characteristic length scale over which the
potential and ion distributions decay within the
EDL is referred to as the Debye length, which
for a symmetric, monovalent electrolyte can be
expressed as
λ! "��� ���2����� . (3)
For low concentration electrolytes (�� < 1
mM) in nanochannels, this characteristic length
can approach and even exceed the height of the
channel. In such situations, it is no longer
appropriate to assume that the ion concentrations
far away from the channel walls (i.e. along the
channel center) are the same as those in the bulk
fluid within the reservoirs supplying the channel.
The centerline concentration in the channel is
instead determined by the potential Ψ' at the
centerline, and the Boltzmann distribution
modifies to � �� exp �� ���Ψ'��� � exp (� ����Ψ � Ψ'���� ). (4)
Using the definition �� ���� � ��� and
assuming a 1D potential profile, we use the
method presented by Baldessari to integrate
Poisson’s equation and find a resulting potential
profile in the different regions of the channel
[18]. It should be noted here that for channels
with modified zeta potentials in the middle
region (see Figure 2), the “bulk” concentration �� of ions in this region will not necessarily be
equal to the supplying inlet or outlet reservoir
concentrations, and must be solved as an
additional unknown using channel-to-well
equilibrium via a species conservation equation.
If the surface charge is known instead of the zeta
potential in a given region of the channel, the
two can be related through the potential gradient
at the wall through the relation
*+ ���� ,-Ψ-./01�. (5)
2.2 Velocity and Electric Fields
The inherently low Reynolds number
associated with flows in nanofluidic devices
allows us to use the incompressible forms of the
Stokes equation and the continuity equation to
describe the conservation of momentum within a
nanochannel for a fluid experiencing an electric
body force,
0 3∇�5 � �6 + ��8; � ∙ 5 0, (6)
where 6 is the pressure within the fluid, 3 is the
dynamic viscosity of the fluid, 5 is the velocity
field, and 8 is the externally applied electric
field. Substituting the charge density from
Poisson’s equation into the electric body force
term in (6) and assuming a 1D fully developed
flow, we obtain the following equation
0 3 ;�<;.� � ;6;= � ��� >? ;�Ψ;.� . (7)
This equation can be directly integrated with a
midplane symmetry condition and a no slip
condition at the wall, resulting in the traditional
1D EOF profile
<�.� �123 -6-= �.� � @.� � �>?ζ3 (1 � Ψ�.�ζ ). (8)
We use the 1D model of Sustarich et al to find
the internal pressure gradients, electric fields,
and resulting flow profiles in the various regions.
This model applies continuity and a known
pressure drop along the channel to solve for the
internal pressure gradients in terms of the electric
fields. The electric fields are then solved with the
constraint that the area averaged electrolyte ion
fluxes due to convection and electromigration
must remain constant throughout the channel
<�AAA + B�̅> �DEFG., (9)
where B HIJKLIMNO [7]. These equations are solved for
the unknown electric fields and the unknown
“bulk” concentration �� of ions in the modified
region. The resulting potential and BGE ion
profiles are then found from the method
described in [18], and the velocity profiles are
calculated from (8).
3. 2D Numerical Model
Commercial finite element simulation
software such as COMSOL Multiphysics has
been used extensively in previous works to
numerically model electrokinetic flows in micro-
and nanofluidics [1,4,7,10,19]. In this paper, we
Excerpt from the Proceedings of the 2016 COMSOL Conference in Boston
use COMSOL
electroosmotically driven flow and
electrophoretic stacking of
nanochannel with a modified zeta potential in the
middle 50% of the channel. The governin
equations are similar
in sections 2.1 and 2.2
more highly coupled Poisson
system of eq
the local ion distributions on the EDL potential.
As such, we don’t explicitly assume a Boltzmann
distribution of ions in our simulation. Instead, we
simply represent the spatial free charge density �� as a local imbal
solution, the concentrations of which are
governed by the Nernst
species
electromigration. Poisson’s equation for the EDL
transverse potential
and the Nern
;�;G
We model (1
PDE” module, and (
species
module within COMSOL. The convection term
in (11
Figure
340,000 mesh elements were used in the various regions to properly resolve the electric double layers, ion transport,
and electroosmotic flow within the channel and reservoirs.
use COMSOL v5.1 to simulate a 2D model of
electroosmotically driven flow and
electrophoretic stacking of
nanochannel with a modified zeta potential in the
middle 50% of the channel. The governin
equations are similar
in sections 2.1 and 2.2
more highly coupled Poisson
system of equations to account for the effect of
the local ion distributions on the EDL potential.
As such, we don’t explicitly assume a Boltzmann
distribution of ions in our simulation. Instead, we
simply represent the spatial free charge density
as a local imbalance of cations and anions in
solution, the concentrations of which are
governed by the Nernst
species experiencing
electromigration. Poisson’s equation for the EDL
transverse potential distribution then bec
���� ��Ψand the Nernst-Planck equation is given by
�;G + 5 ∙ �� P�We model (10) using a “Coefficient Form
PDE” module, and (
species using the “Transport of Diluted Species”
module within COMSOL. The convection term
1) is due to the advective transport of ions
Figure 2: Diagram of the
340,000 mesh elements were used in the various regions to properly resolve the electric double layers, ion transport,
and electroosmotic flow within the channel and reservoirs.
v5.1 to simulate a 2D model of
electroosmotically driven flow and
electrophoretic stacking of sample ions in a
nanochannel with a modified zeta potential in the
middle 50% of the channel. The governin
equations are similar to the equations presented
in sections 2.1 and 2.2; however, we use the
more highly coupled Poisson-
uations to account for the effect of
the local ion distributions on the EDL potential.
As such, we don’t explicitly assume a Boltzmann
distribution of ions in our simulation. Instead, we
simply represent the spatial free charge density
ance of cations and anions in
solution, the concentrations of which are
governed by the Nernst-Planck equation for a
experiencing convection, diffusion, and
electromigration. Poisson’s equation for the EDL
distribution then bec
Ψ ���� � ���, Planck equation is given by
� ∙ ��� + ��������) using a “Coefficient Form
PDE” module, and (11) for the various ionic
“Transport of Diluted Species”
module within COMSOL. The convection term
due to the advective transport of ions
Diagram of the numerical mesh and boundary conditions used in the COMSOL simulations. Approximately
340,000 mesh elements were used in the various regions to properly resolve the electric double layers, ion transport,
and electroosmotic flow within the channel and reservoirs.
v5.1 to simulate a 2D model of
electroosmotically driven flow and the
sample ions in a
nanochannel with a modified zeta potential in the
middle 50% of the channel. The governing
e equations presented
; however, we use the
-Nernst-Planck
uations to account for the effect of
the local ion distributions on the EDL potential.
As such, we don’t explicitly assume a Boltzmann
distribution of ions in our simulation. Instead, we
simply represent the spatial free charge density
ance of cations and anions in
solution, the concentrations of which are
Planck equation for a
convection, diffusion, and
electromigration. Poisson’s equation for the EDL
distribution then becomes
� (10)
Planck equation is given by
�V + ��� �. (11)
) using a “Coefficient Form
for the various ionic
“Transport of Diluted Species”
module within COMSOL. The convection term
due to the advective transport of ions
numerical mesh and boundary conditions used in the COMSOL simulations. Approximately
340,000 mesh elements were used in the various regions to properly resolve the electric double layers, ion transport,
and electroosmotic flow within the channel and reservoirs.
v5.1 to simulate a 2D model of
the
sample ions in a
nanochannel with a modified zeta potential in the
g
e equations presented
; however, we use the
Planck
uations to account for the effect of
the local ion distributions on the EDL potential.
As such, we don’t explicitly assume a Boltzmann
distribution of ions in our simulation. Instead, we
simply represent the spatial free charge density
ance of cations and anions in
solution, the concentrations of which are
Planck equation for a
convection, diffusion, and
electromigration. Poisson’s equation for the EDL
) using a “Coefficient Form
for the various ionic
“Transport of Diluted Species”
module within COMSOL. The convection term
due to the advective transport of ions
from the electroosmotic flow,
the Stokes equation and mass continuity
This
COMSOL using the “Creeping Flow” module.
Finally, Ohm’s Law
modeled with the “Electric Currents” module
describe the electric field within the fluid
where
electrical conductivity, and
applied
depends on the local number of charge carriers,
and contains components related to the
convective and conductive
channel [18
terms of the local ba
as
The first term
to a nonzero charge being advected downstream
by the EOF, while the second term represents the
current generated by the electromigration of
individual
the presence of the external field.
numerical mesh and boundary conditions used in the COMSOL simulations. Approximately
340,000 mesh elements were used in the various regions to properly resolve the electric double layers, ion transport,
and electroosmotic flow within the channel and reservoirs.
from the electroosmotic flow,
the Stokes equation and mass continuity
R0 3∇�5This electroosmotic
COMSOL using the “Creeping Flow” module.
Finally, Ohm’s Law
modeled with the “Electric Currents” module
describe the electric field within the fluid
RS *�8where S is the local current density,
electrical conductivity, and
applied potential. The electrical conductivity
depends on the local number of charge carriers,
and contains components related to the
convective and conductive
channel [18]. The conductivity can be written in
terms of the local ba
*T <?���� �>?
The first term in (14)
to a nonzero charge being advected downstream
by the EOF, while the second term represents the
current generated by the electromigration of
individual background electrolyte (
the presence of the external field.
numerical mesh and boundary conditions used in the COMSOL simulations. Approximately
340,000 mesh elements were used in the various regions to properly resolve the electric double layers, ion transport,
from the electroosmotic flow, and
the Stokes equation and mass continuity
5 � �6 + ���� �� ∙ 5 0.electroosmotic flow field is modeled in
COMSOL using the “Creeping Flow” module.
Finally, Ohm’s Law and current continuity are
modeled with the “Electric Currents” module
describe the electric field within the fluid
8; 8 ��� ∙ S 0,is the local current density,
electrical conductivity, and U is the externally
. The electrical conductivity
depends on the local number of charge carriers,
and contains components related to the
convective and conductive currents in the
]. The conductivity can be written in
terms of the local background ion concentrations
� � ��� + ����� ����in (14) represents the current due
to a nonzero charge being advected downstream
by the EOF, while the second term represents the
current generated by the electromigration of
background electrolyte (
the presence of the external field.
numerical mesh and boundary conditions used in the COMSOL simulations. Approximately
340,000 mesh elements were used in the various regions to properly resolve the electric double layers, ion transport,
and is coupled to
the Stokes equation and mass continuity
���8, (12
flow field is modeled in
COMSOL using the “Creeping Flow” module.
and current continuity are
modeled with the “Electric Currents” module to
describe the electric field within the fluid
�U, (13
is the local current density, *� is the
is the externally
. The electrical conductivity
depends on the local number of charge carriers,
and contains components related to the
currents in the
]. The conductivity can be written in
ckground ion concentrations
� + ���PV. (14
represents the current due
to a nonzero charge being advected downstream
by the EOF, while the second term represents the
current generated by the electromigration of
background electrolyte (BGE) ions in
For thin EDLs,
numerical mesh and boundary conditions used in the COMSOL simulations. Approximately
340,000 mesh elements were used in the various regions to properly resolve the electric double layers, ion transport,
to
2)
flow field is modeled in
COMSOL using the “Creeping Flow” module.
and current continuity are
to
3)
is the
is the externally
. The electrical conductivity
depends on the local number of charge carriers,
and contains components related to the
currents in the
]. The conductivity can be written in
ckground ion concentrations
14)
represents the current due
to a nonzero charge being advected downstream
by the EOF, while the second term represents the
current generated by the electromigration of
ions in
For thin EDLs,
numerical mesh and boundary conditions used in the COMSOL simulations. Approximately
Excerpt from the Proceedings of the 2016 COMSOL Conference in Boston
most of
where
compared to the second. However, we are
investigating nanochannels with electrolyte
concentrations sufficiently low to cause
significant overlapping of the EDLs, so the
contribution of the local charge density to the
electrical conductivity
A
340,000 distributed mapped
triangular elements was employed throughout
the channel and reservoirs
was used to
gradients withi
regions while still allowing for computations that
were both time and memory efficient.
depicts
and boundary conditions for the nanochannel and
supplying reservoirs.
simulations was KCl, with
and Pdiffusivity was
unless otherwise noted, the sample charge was
fixed at
4. Results
In order to verify that our numerical model
produces reasonable results, we first compare the
2D and 1D models for a relatively simple case of
non-overlapping EDLs. We simulated a 0.5 mm
long, 100 nm tall channel filled with a solution
of 2.5mM KCl, corres
of about
potential
EOF with a nominal electric field of 10,000 V/m.
The unmodified and modified zeta potentials
were -
Figure
excellent agreement for (a) the transverse potential, (b) BGE ion, and (c) velocity profiles in both region 1 (blue) and
region 2 (red). Discrepancies in (d) the centerline BGE
most of the fluid
where �� ��, and the first ter
compared to the second. However, we are
investigating nanochannels with electrolyte
concentrations sufficiently low to cause
significant overlapping of the EDLs, so the
contribution of the local charge density to the
electrical conductivity
finite element mesh of approximately
340,000 distributed mapped
triangular elements was employed throughout
the channel and reservoirs
was used to ensure proper resolution of fine
gradients within the EDLs and near transition
regions while still allowing for computations that
re both time and memory efficient.
depicts a diagram of the 2D model with the mesh
and boundary conditions for the nanochannel and
supplying reservoirs.
simulations was KCl, with PWX 2.03 x 10
diffusivity was fixed at
unless otherwise noted, the sample charge was
fixed at z = -2.
Results
In order to verify that our numerical model
produces reasonable results, we first compare the
2D and 1D models for a relatively simple case of
overlapping EDLs. We simulated a 0.5 mm
long, 100 nm tall channel filled with a solution
of 2.5mM KCl, corres
of about λ! 6.1 nm. An externally applied
potential of 5 V was used to drive the simulated
EOF with a nominal electric field of 10,000 V/m.
The unmodified and modified zeta potentials
-25 mV and -5 mV, respectively.
Figure 3: Comparison of thin EDL ana
excellent agreement for (a) the transverse potential, (b) BGE ion, and (c) velocity profiles in both region 1 (blue) and
region 2 (red). Discrepancies in (d) the centerline BGE
the fluid remains electrically neutral
and the first term is negligible
compared to the second. However, we are
investigating nanochannels with electrolyte
concentrations sufficiently low to cause
significant overlapping of the EDLs, so the
contribution of the local charge density to the
electrical conductivity cannot be neglected [
finite element mesh of approximately
340,000 distributed mapped elements and
triangular elements was employed throughout
the channel and reservoirs. This custom mesh
ensure proper resolution of fine
n the EDLs and near transition
regions while still allowing for computations that
re both time and memory efficient.
a diagram of the 2D model with the mesh
and boundary conditions for the nanochannel and
supplying reservoirs. The electrolyte us
simulations was KCl, with PY 1.96 x 10
2.03 x 10-9 m2/s.
fixed at PZ 1 x 10
unless otherwise noted, the sample charge was
In order to verify that our numerical model
produces reasonable results, we first compare the
2D and 1D models for a relatively simple case of
overlapping EDLs. We simulated a 0.5 mm
long, 100 nm tall channel filled with a solution
of 2.5mM KCl, corresponding to a Debye length
6.1 nm. An externally applied
of 5 V was used to drive the simulated
EOF with a nominal electric field of 10,000 V/m.
The unmodified and modified zeta potentials
5 mV, respectively.
Comparison of thin EDL ana
excellent agreement for (a) the transverse potential, (b) BGE ion, and (c) velocity profiles in both region 1 (blue) and
region 2 (red). Discrepancies in (d) the centerline BGE
remains electrically neutral
m is negligible
compared to the second. However, we are
investigating nanochannels with electrolyte
concentrations sufficiently low to cause
significant overlapping of the EDLs, so the
contribution of the local charge density to the
cannot be neglected [19].
finite element mesh of approximately
elements and
triangular elements was employed throughout
This custom mesh
ensure proper resolution of fine
n the EDLs and near transition
regions while still allowing for computations that
re both time and memory efficient. Figure 2
a diagram of the 2D model with the mesh
and boundary conditions for the nanochannel and
olyte used in all
1.96 x 10-9 m2/s
The sample
1 x 10-9 m2/s and,
unless otherwise noted, the sample charge was
In order to verify that our numerical model
produces reasonable results, we first compare the
2D and 1D models for a relatively simple case of
overlapping EDLs. We simulated a 0.5 mm
long, 100 nm tall channel filled with a solution
ponding to a Debye length
6.1 nm. An externally applied
of 5 V was used to drive the simulated
EOF with a nominal electric field of 10,000 V/m.
The unmodified and modified zeta potentials
5 mV, respectively.
Comparison of thin EDL analytical (solid lines) vs. simulation results (open circles). The profiles show
excellent agreement for (a) the transverse potential, (b) BGE ion, and (c) velocity profiles in both region 1 (blue) and
region 2 (red). Discrepancies in (d) the centerline BGE
remains electrically neutral
m is negligible
compared to the second. However, we are
investigating nanochannels with electrolyte
concentrations sufficiently low to cause
significant overlapping of the EDLs, so the
contribution of the local charge density to the
finite element mesh of approximately
elements and
triangular elements was employed throughout
This custom mesh
ensure proper resolution of fine
n the EDLs and near transition
regions while still allowing for computations that
Figure 2
a diagram of the 2D model with the mesh
and boundary conditions for the nanochannel and
ed in all
/s
The sample
/s and,
unless otherwise noted, the sample charge was
In order to verify that our numerical model
produces reasonable results, we first compare the
2D and 1D models for a relatively simple case of
overlapping EDLs. We simulated a 0.5 mm
long, 100 nm tall channel filled with a solution
ponding to a Debye length
6.1 nm. An externally applied
of 5 V was used to drive the simulated
EOF with a nominal electric field of 10,000 V/m.
The unmodified and modified zeta potentials
Figure
vertical profiles of the EDL potential, BGE salt
concentration
centerline BGE salt concentration
axial transport equation
The profiles demonst
between the simulated and analytical results,
with perhaps the slight exception of the
centerline profile near the zeta potential
transitions. This is to be expected, however, as
the 1D analytical model cannot account for
localized
dispersion near the transition
We validated our model further for a case
with thick electric double layers, comparing
various profiles with the 1D analytical model as
the zeta potential in the middle of the channel
was varied
show exce
charge density profiles, although the velocity
profiles seem to increasingly deviate for the
more uniform cases. This is likely due to the fact
that the analytical r
difference between channel inlet and outlet,
whereas in the simulation and in
situation
decelerating in the respective
cause an
channel
would become more prominent for thicker EDL
cases due to the nonzero el
everywhere, as well as for faster
hence the higher deviation for the more uniform
cases.
Ou
that the sample stacking only occurs when the
nonuniformities in velocity, potential, and ion
distributions throughout the channel are
lytical (solid lines) vs. simulation results (open circles). The profiles show
excellent agreement for (a) the transverse potential, (b) BGE ion, and (c) velocity profiles in both region 1 (blue) and
region 2 (red). Discrepancies in (d) the centerline BGE ion profile are likely due to 2D effects such as dispersion.
Figure 3 shows a comparison of the resulting
vertical profiles of the EDL potential, BGE salt
concentration, and
centerline BGE salt concentration
axial transport equation
The profiles demonst
between the simulated and analytical results,
with perhaps the slight exception of the
centerline profile near the zeta potential
transitions. This is to be expected, however, as
the 1D analytical model cannot account for
localized 2D effects such as flow focusing and
dispersion near the transition
We validated our model further for a case
with thick electric double layers, comparing
various profiles with the 1D analytical model as
the zeta potential in the middle of the channel
as varied in a 0.01mM solution
show excellent agreement for the
charge density profiles, although the velocity
profiles seem to increasingly deviate for the
more uniform cases. This is likely due to the fact
that the analytical r
difference between channel inlet and outlet,
reas in the simulation and in
situations the effect of the fluid accelerating and
decelerating in the respective
cause an adverse pressure
channel and slow the fluid slightly. This effect
would become more prominent for thicker EDL
cases due to the nonzero el
everywhere, as well as for faster
hence the higher deviation for the more uniform
cases.
Our simulation results in Figure 4 also show
that the sample stacking only occurs when the
nonuniformities in velocity, potential, and ion
distributions throughout the channel are
lytical (solid lines) vs. simulation results (open circles). The profiles show
excellent agreement for (a) the transverse potential, (b) BGE ion, and (c) velocity profiles in both region 1 (blue) and
ion profile are likely due to 2D effects such as dispersion.
shows a comparison of the resulting
vertical profiles of the EDL potential, BGE salt
and axial velocity. A plot of the
centerline BGE salt concentration
axial transport equation from [7] is also included.
The profiles demonstrate excellent agreement
between the simulated and analytical results,
with perhaps the slight exception of the
centerline profile near the zeta potential
transitions. This is to be expected, however, as
the 1D analytical model cannot account for
2D effects such as flow focusing and
dispersion near the transitions.
We validated our model further for a case
with thick electric double layers, comparing
various profiles with the 1D analytical model as
the zeta potential in the middle of the channel
in a 0.01mM solution
llent agreement for the
charge density profiles, although the velocity
profiles seem to increasingly deviate for the
more uniform cases. This is likely due to the fact
that the analytical results assumed zero pressure
difference between channel inlet and outlet,
reas in the simulation and in
the effect of the fluid accelerating and
decelerating in the respective reservoirs would
adverse pressure gradient
and slow the fluid slightly. This effect
would become more prominent for thicker EDL
cases due to the nonzero electric body force
everywhere, as well as for faster
hence the higher deviation for the more uniform
r simulation results in Figure 4 also show
that the sample stacking only occurs when the
nonuniformities in velocity, potential, and ion
distributions throughout the channel are
lytical (solid lines) vs. simulation results (open circles). The profiles show
excellent agreement for (a) the transverse potential, (b) BGE ion, and (c) velocity profiles in both region 1 (blue) and
ion profile are likely due to 2D effects such as dispersion.
shows a comparison of the resulting
vertical profiles of the EDL potential, BGE salt
velocity. A plot of the
centerline BGE salt concentration based on a 1D
is also included.
rate excellent agreement
between the simulated and analytical results,
with perhaps the slight exception of the
centerline profile near the zeta potential
transitions. This is to be expected, however, as
the 1D analytical model cannot account for
2D effects such as flow focusing and
We validated our model further for a case
with thick electric double layers, comparing
various profiles with the 1D analytical model as
the zeta potential in the middle of the channel
in a 0.01mM solution. The results
llent agreement for the potential and
charge density profiles, although the velocity
profiles seem to increasingly deviate for the
more uniform cases. This is likely due to the fact
esults assumed zero pressure
difference between channel inlet and outlet,
reas in the simulation and in experimental
the effect of the fluid accelerating and
reservoirs would
gradient across the
and slow the fluid slightly. This effect
would become more prominent for thicker EDL
ectric body force
everywhere, as well as for faster-moving flows;
hence the higher deviation for the more uniform
r simulation results in Figure 4 also show
that the sample stacking only occurs when the
nonuniformities in velocity, potential, and ion
distributions throughout the channel are
lytical (solid lines) vs. simulation results (open circles). The profiles show
excellent agreement for (a) the transverse potential, (b) BGE ion, and (c) velocity profiles in both region 1 (blue) and
ion profile are likely due to 2D effects such as dispersion.
shows a comparison of the resulting
vertical profiles of the EDL potential, BGE salt
velocity. A plot of the
1D
is also included.
rate excellent agreement
between the simulated and analytical results,
with perhaps the slight exception of the
centerline profile near the zeta potential
transitions. This is to be expected, however, as
the 1D analytical model cannot account for
2D effects such as flow focusing and
We validated our model further for a case
with thick electric double layers, comparing
various profiles with the 1D analytical model as
the zeta potential in the middle of the channel
. The results
potential and
charge density profiles, although the velocity
profiles seem to increasingly deviate for the
more uniform cases. This is likely due to the fact
esults assumed zero pressure
difference between channel inlet and outlet,
experimental
the effect of the fluid accelerating and
reservoirs would
across the
and slow the fluid slightly. This effect
would become more prominent for thicker EDL
ectric body force
moving flows;
hence the higher deviation for the more uniform
r simulation results in Figure 4 also show
that the sample stacking only occurs when the
nonuniformities in velocity, potential, and ion
Excerpt from the Proceedings of the 2016 COMSOL Conference in Boston
sufficiently large. This requires thick electric
double layers, such that the background ion
distributions and resulting electromigrative
fluxes are modified sufficiently near the
centerline.
electrostatic interactions of the EDL are confined
near the wall and a majority of the fluid is at the
bulk concentration and bulk conductivity, which
leads to uniform electric fields and sample
fluxes. Additionally, a cha
potential and conductivity distributions will have
a uniform electrochemical potential and not
allow for any local ion enrichment or depletion
along the length of the channel. A nonuniform
surface potential distribution and thick EDL
thus essential to induce the heterogeneity
required within the single buffer solution to
produce the gradients that lead to stacking.
Highly charged sample ions are more strongly
affected by these field gradients and can be
effectively concentrated t
Figure 5 depicts the
2D sample concentration profile within the
channel, showing
sample
step change in zeta potential occurs.
thick electr
repelled towards the center of the channel,
increasing the local enhancement along the
centerline.
the centerline is nonzero due to the thick EDLs,
so there is an additional
along the channel
one region to the next.
Figure
(a) the potential, (b) the charge density, and (c) the
enhancement ratios are shown in (d) for varying zeta potential ratios and EDL thicknesses, and in (e) for varying zeta
potential and sample charge. The zeta potential in region 1 was fixed a
sufficiently large. This requires thick electric
double layers, such that the background ion
distributions and resulting electromigrative
fluxes are modified sufficiently near the
centerline. For thin electric double layers, the
electrostatic interactions of the EDL are confined
near the wall and a majority of the fluid is at the
bulk concentration and bulk conductivity, which
leads to uniform electric fields and sample
fluxes. Additionally, a cha
potential and conductivity distributions will have
a uniform electrochemical potential and not
allow for any local ion enrichment or depletion
along the length of the channel. A nonuniform
surface potential distribution and thick EDL
thus essential to induce the heterogeneity
required within the single buffer solution to
produce the gradients that lead to stacking.
Highly charged sample ions are more strongly
affected by these field gradients and can be
effectively concentrated t
Figure 5 depicts the
2D sample concentration profile within the
channel, showing
sample stacks near an interface where a smooth
step change in zeta potential occurs.
thick electric double layers,
repelled towards the center of the channel,
increasing the local enhancement along the
centerline. The intrinsic EDL potential
the centerline is nonzero due to the thick EDLs,
so there is an additional
along the channel as the flow transitions from
one region to the next.
Figure 4: Simulation results for thick EDLs. Analytical (solid lines) vs. simulation (solid circles) results are shown for
(a) the potential, (b) the charge density, and (c) the
enhancement ratios are shown in (d) for varying zeta potential ratios and EDL thicknesses, and in (e) for varying zeta
potential and sample charge. The zeta potential in region 1 was fixed a
sufficiently large. This requires thick electric
double layers, such that the background ion
distributions and resulting electromigrative
fluxes are modified sufficiently near the
thin electric double layers, the
electrostatic interactions of the EDL are confined
near the wall and a majority of the fluid is at the
bulk concentration and bulk conductivity, which
leads to uniform electric fields and sample
fluxes. Additionally, a channel with uniform wall
potential and conductivity distributions will have
a uniform electrochemical potential and not
allow for any local ion enrichment or depletion
along the length of the channel. A nonuniform
surface potential distribution and thick EDL
thus essential to induce the heterogeneity
required within the single buffer solution to
produce the gradients that lead to stacking.
Highly charged sample ions are more strongly
affected by these field gradients and can be
effectively concentrated to higher levels.
Figure 5 depicts the temporal evolution of
2D sample concentration profile within the
channel, showing how a negatively charged
near an interface where a smooth
step change in zeta potential occurs.
ic double layers, the sample is
repelled towards the center of the channel,
increasing the local enhancement along the
The intrinsic EDL potential
the centerline is nonzero due to the thick EDLs,
so there is an additional axial potentia
as the flow transitions from
one region to the next. This additional potential
Simulation results for thick EDLs. Analytical (solid lines) vs. simulation (solid circles) results are shown for
(a) the potential, (b) the charge density, and (c) the
enhancement ratios are shown in (d) for varying zeta potential ratios and EDL thicknesses, and in (e) for varying zeta
potential and sample charge. The zeta potential in region 1 was fixed a
sufficiently large. This requires thick electric
double layers, such that the background ion
distributions and resulting electromigrative
fluxes are modified sufficiently near the
thin electric double layers, the
electrostatic interactions of the EDL are confined
near the wall and a majority of the fluid is at the
bulk concentration and bulk conductivity, which
leads to uniform electric fields and sample
nnel with uniform wall
potential and conductivity distributions will have
a uniform electrochemical potential and not
allow for any local ion enrichment or depletion
along the length of the channel. A nonuniform
surface potential distribution and thick EDLs are
thus essential to induce the heterogeneity
required within the single buffer solution to
produce the gradients that lead to stacking.
Highly charged sample ions are more strongly
affected by these field gradients and can be
o higher levels.
temporal evolution of a
2D sample concentration profile within the
how a negatively charged
near an interface where a smooth
step change in zeta potential occurs. Due to the
the sample is
repelled towards the center of the channel,
increasing the local enhancement along the
The intrinsic EDL potential Ψ along
the centerline is nonzero due to the thick EDLs,
axial potential gradient
as the flow transitions from
This additional potential
Simulation results for thick EDLs. Analytical (solid lines) vs. simulation (solid circles) results are shown for
(a) the potential, (b) the charge density, and (c) the velocity profiles for varying zeta potentials in region 2. Sample
enhancement ratios are shown in (d) for varying zeta potential ratios and EDL thicknesses, and in (e) for varying zeta
potential and sample charge. The zeta potential in region 1 was fixed a
sufficiently large. This requires thick electric
double layers, such that the background ion
distributions and resulting electromigrative
fluxes are modified sufficiently near the
thin electric double layers, the
electrostatic interactions of the EDL are confined
near the wall and a majority of the fluid is at the
bulk concentration and bulk conductivity, which
leads to uniform electric fields and sample
nnel with uniform wall
potential and conductivity distributions will have
a uniform electrochemical potential and not
allow for any local ion enrichment or depletion
along the length of the channel. A nonuniform
s are
thus essential to induce the heterogeneity
required within the single buffer solution to
produce the gradients that lead to stacking.
Highly charged sample ions are more strongly
affected by these field gradients and can be
a
2D sample concentration profile within the
how a negatively charged
near an interface where a smooth
Due to the
the sample is
repelled towards the center of the channel,
increasing the local enhancement along the
along
the centerline is nonzero due to the thick EDLs,
gradient
as the flow transitions from
This additional potential
gradient
axial gradient in the applied potential, and the net
electric field can change direction locally
result
electrophoretic trapping region, as shown in
Figure 5.
diffusion
the transport of the sample through the channel.
The diffusi
electromigrative flux and the
the enhancement region
steady state.
transition, the opposite
potential gradient
external field
accelerated, creating a local
5. Conclusions
In this work, we use
Multiphysics to model the 2D electroosmotic
flow of a
electrophoretic stacking of sample ions in a
nanochannel with selectively modified surface
charge. We show
and focusing effects only occur in channels with
sufficiently large step changes in zeta potential,
and for cases i
large relative to the channel height. Our
approach can potentially achieve
hundred
higher than those limited by conductivity ratios
in conventional FASS[
field, potential,
Simulation results for thick EDLs. Analytical (solid lines) vs. simulation (solid circles) results are shown for
velocity profiles for varying zeta potentials in region 2. Sample
enhancement ratios are shown in (d) for varying zeta potential ratios and EDL thicknesses, and in (e) for varying zeta
potential and sample charge. The zeta potential in region 1 was fixed a
gradient can be larger in magnitude than the
axial gradient in the applied potential, and the net
electric field can change direction locally
result. This enhances the s
electrophoretic trapping region, as shown in
Figure 5. Once the
diffusion becomes a significant driving factor in
the transport of the sample through the channel.
The diffusive flux
electromigrative flux and the
the enhancement region
steady state. Near the other zeta potential
transition, the opposite
potential gradient is in the same
external field. Sample ions here are
accelerated, creating a local
Conclusions
In this work, we use
Multiphysics to model the 2D electroosmotic
flow of a dilute background electrolyte and
electrophoretic stacking of sample ions in a
nanochannel with selectively modified surface
charge. We showed
and focusing effects only occur in channels with
sufficiently large step changes in zeta potential,
and for cases in which the EDLs are sufficiently
large relative to the channel height. Our
approach can potentially achieve
hundred-fold sample enhancement ratios, notably
higher than those limited by conductivity ratios
in conventional FASS[
, potential, and ion distributions were
Simulation results for thick EDLs. Analytical (solid lines) vs. simulation (solid circles) results are shown for
velocity profiles for varying zeta potentials in region 2. Sample
enhancement ratios are shown in (d) for varying zeta potential ratios and EDL thicknesses, and in (e) for varying zeta
potential and sample charge. The zeta potential in region 1 was fixed at -100 mV for these simulations.
can be larger in magnitude than the
axial gradient in the applied potential, and the net
electric field can change direction locally
This enhances the stacking
electrophoretic trapping region, as shown in
nce the sample starts to
becomes a significant driving factor in
the transport of the sample through the channel.
ve flux eventually balances the
electromigrative flux and the convective flux in
the enhancement region as the system reaches a
Near the other zeta potential
transition, the opposite effect occurs as the
is in the same
Sample ions here are
accelerated, creating a localized depletion region.
In this work, we use
Multiphysics to model the 2D electroosmotic
background electrolyte and
electrophoretic stacking of sample ions in a
nanochannel with selectively modified surface
ed that these particular stacking
and focusing effects only occur in channels with
sufficiently large step changes in zeta potential,
n which the EDLs are sufficiently
large relative to the channel height. Our
approach can potentially achieve
fold sample enhancement ratios, notably
higher than those limited by conductivity ratios
in conventional FASS[7,8]. Resulting veloc
and ion distributions were
Simulation results for thick EDLs. Analytical (solid lines) vs. simulation (solid circles) results are shown for
velocity profiles for varying zeta potentials in region 2. Sample
enhancement ratios are shown in (d) for varying zeta potential ratios and EDL thicknesses, and in (e) for varying zeta
100 mV for these simulations.
can be larger in magnitude than the
axial gradient in the applied potential, and the net
electric field can change direction locally as
acking and creates an
electrophoretic trapping region, as shown in
sample starts to accumulate,
becomes a significant driving factor in
the transport of the sample through the channel.
eventually balances the
convective flux in
as the system reaches a
Near the other zeta potential
effect occurs as the EDL
is in the same direction as the
Sample ions here are further
depletion region.
In this work, we used COMSOL
Multiphysics to model the 2D electroosmotic
background electrolyte and the
electrophoretic stacking of sample ions in a
nanochannel with selectively modified surface
that these particular stacking
and focusing effects only occur in channels with
sufficiently large step changes in zeta potential,
n which the EDLs are sufficiently
large relative to the channel height. Our
approach can potentially achieve several
fold sample enhancement ratios, notably
higher than those limited by conductivity ratios
]. Resulting velocity
and ion distributions were
Simulation results for thick EDLs. Analytical (solid lines) vs. simulation (solid circles) results are shown for
velocity profiles for varying zeta potentials in region 2. Sample
enhancement ratios are shown in (d) for varying zeta potential ratios and EDL thicknesses, and in (e) for varying zeta
100 mV for these simulations.
can be larger in magnitude than the
axial gradient in the applied potential, and the net
a
and creates an
electrophoretic trapping region, as shown in
accumulate,
becomes a significant driving factor in
the transport of the sample through the channel.
eventually balances the
convective flux in
as the system reaches a
Near the other zeta potential
EDL
as the
further
depletion region.
COMSOL
Multiphysics to model the 2D electroosmotic
the
electrophoretic stacking of sample ions in a
nanochannel with selectively modified surface
that these particular stacking
and focusing effects only occur in channels with
sufficiently large step changes in zeta potential,
n which the EDLs are sufficiently
large relative to the channel height. Our
several
fold sample enhancement ratios, notably
higher than those limited by conductivity ratios
ity
Simulation results for thick EDLs. Analytical (solid lines) vs. simulation (solid circles) results are shown for
Excerpt from the Proceedings of the 2016 COMSOL Conference in Boston
Figure
electrophoretic trapping of particles in a simulation, (c) steady state fluxes along the c
averaged time
gradient is visible in the positive electrophoretic flux of the negative sample in (d), the peaks near the t
locations in (c),
validated through comparison with existing
analytical techniques to solve the 1D Poisson
Boltzmann equation, Stokes equation, and
Nernst
These results provide encouraging
indications that it is possible to perform
stationary field
preconcentration in nanochannels without using
multiple electrolyte solutions, but by simply
inducing electric field gradients through
tailoring of
embedded electrodes. The resulting enhancement
in our simulations
microchannel
rivals
11], revealing
sample preconcentration in nanofluidic devices.
6. References 1. Yu
nanofluidic concentrator
(2015)
2. Hsu W, Harvie D J, Davidson M R, Jeong H,
Goldys E M, and Ing
focusing and separation in a silica nanofluidic channel
with a non
14, 3539
3. Stein D, Deurvorst Z, van der Heyden F H J,
Koopmans W
Electrokinetic Concentration of DNA Polymers in
Nanofluidic Channels
Figure 5: (a) Transient evolution of 2D sample concentration profile within the channel, (b) a diagram depicting
electrophoretic trapping of particles in a simulation, (c) steady state fluxes along the c
averaged time-dependent sample fluxes at the location of maximum enhancement. The effect of the axial EDL potential
gradient is visible in the positive electrophoretic flux of the negative sample in (d), the peaks near the t
ons in (c), and flux lines near the electrophoretic trap in
validated through comparison with existing
analytical techniques to solve the 1D Poisson
Boltzmann equation, Stokes equation, and
Nernst-Planck equation [
These results provide encouraging
indications that it is possible to perform
stationary field
preconcentration in nanochannels without using
multiple electrolyte solutions, but by simply
inducing electric field gradients through
ing of wall surface charge uniformity via
embedded electrodes. The resulting enhancement
in our simulations can
microchannel-based
rivals that of similar
revealing another pro
sample preconcentration in nanofluidic devices.
. References
1. Yu M, Hou Y, Zhou H, and Yao S,
nanofluidic concentrator
2. Hsu W, Harvie D J, Davidson M R, Jeong H,
Goldys E M, and Inglis
focusing and separation in a silica nanofluidic channel
with a non-uniform electroosmotic flow
3539-49 (2014)
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(a) Transient evolution of 2D sample concentration profile within the channel, (b) a diagram depicting
electrophoretic trapping of particles in a simulation, (c) steady state fluxes along the c
dependent sample fluxes at the location of maximum enhancement. The effect of the axial EDL potential
gradient is visible in the positive electrophoretic flux of the negative sample in (d), the peaks near the t
and flux lines near the electrophoretic trap in
validated through comparison with existing
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preconcentration in nanochannels without using
multiple electrolyte solutions, but by simply
inducing electric field gradients through
wall surface charge uniformity via
embedded electrodes. The resulting enhancement
can exceed that of
stacking mechanisms
that of similar nanoscale methods [
another promising technique for
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Nano Letters 10
(a) Transient evolution of 2D sample concentration profile within the channel, (b) a diagram depicting
electrophoretic trapping of particles in a simulation, (c) steady state fluxes along the c
dependent sample fluxes at the location of maximum enhancement. The effect of the axial EDL potential
gradient is visible in the positive electrophoretic flux of the negative sample in (d), the peaks near the t
and flux lines near the electrophoretic trap in
validated through comparison with existing
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(a) Transient evolution of 2D sample concentration profile within the channel, (b) a diagram depicting
electrophoretic trapping of particles in a simulation, (c) steady state fluxes along the c
dependent sample fluxes at the location of maximum enhancement. The effect of the axial EDL potential
gradient is visible in the positive electrophoretic flux of the negative sample in (d), the peaks near the t
and flux lines near the electrophoretic trap in (b).
validated through comparison with existing
Boltzmann equation, Stokes equation, and
These results provide encouraging
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multiple electrolyte solutions, but by simply
the
wall surface charge uniformity via
embedded electrodes. The resulting enhancement
traditional
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7. Acknowledgements
We greatly acknowledge our funding
sources, the Institute for Collaborative
Biotechnologies through grant W911NF-09-001
from the U.S. Army Research Office, and grant
DAAD19-03-D-0004 from the U.S. Army
Research Office.
Excerpt from the Proceedings of the 2016 COMSOL Conference in Boston