Reversed flow at low frequencies in a microfabricated AC electrokinetic
  pump
Reversed flow at low frequencies in a microfabricated AC electrokinetic pump
Misha Marie Gregersen, Laurits Højgaard Olesen, Anders Brask, Mikkel Fougt Hansen, and Henrik Bruus
MIC – Department of Micro and Nanotechnology, Technical University of Denmark
DTU bldg. 345 east, DK-2800 Kongens Lyngby, Denmark
(Dated: 29 Marts 2007)
Microfluidic chips have been fabricated to study electrokinetic pumping generated by a low voltage
AC signal applied to an asymmetric electrode array. A measurement procedure has been established
and followed carefully resulting in a high degree of reproducibility of the measurements. Depending
on the ionic concentration as well as the amplitude of the applied voltage, the observed direction
of the DC flow component is either forward or reverse. The impedance spectrum has been thor-
oughly measured and analyzed in terms of an equivalent circuit diagram. Our observations agree
qualitatively, but not quantitatively, with theoretical models published in the literature.
I. INTRODUCTION
The recent interest in AC electrokinetic micropumps
was initiated by experimental observations by Green,
Gonzales et al. of fluid motion induced by AC electroos-
mosis over pairs of microelectrodes [1, 2, 3] and by a the-
oretical prediction by Ajdari that the same mechanism
would generate flow above an electrode array [4]. Brown
et al. [5] demonstrated experimentally pumping of elec-
trolyte with a low voltage, AC biased electrode array,
and soon after the same effect was reported by a num-
ber of other groups observing flow velocities of the order
of mm/s [6, 7, 8, 9, 10, 11, 12, 13]. Several theoretical
models have been proposed parallel to the experimental
observations [14, 15, 16]. However, so far not all aspects
of the flow-generating mechanisms have been explained.
Studer et al. [10] made a thorough investigation of flow
dependence on electrolyte concentration, driving voltage
and frequency for a characteristic system. In this work
a reversal of the pumping direction for frequencies above
10 kHz and rms voltages above 2 V was reported. For
a travelling wave device Ramos et al. [12] observed re-
versal of the pumping direction at 1 kHz and voltages
above 2 V. The reason for this reversal is not yet fully
understood and the goal of this work is to contribute
with further experimental observations of reversing flow
for other parameters than those reported previously.
An integrated electrokinetic AC driven micropump has
been fabricated and studied. The design follows Studer
et al. [10], where an asymmetric array of electrodes covers
the channel bottom in one section of a closed pumping
loop. Pumping velocities are measured in another sec-
tion of the channel without electrodes. In this way elec-
trophoretic interaction between the beads used as flow
markers and the electrodes is avoided. In contrast to the
soft lithography utilized by Studer et al., we use more
well-defined MEMS fabrication techniques in Pyrex glass.
This results in a very robust system, which exhibits sta-
ble properties and remains functional over time periods
extending up to a year. Furthermore, we have a larger
electrode coverage of the total channel length allowing
for the detection of smaller pumping velocities. Our im-
proved design has led to the observation of a new phe-
nomenon, namely the reversing of the flow at low voltages
and low frequencies. The electrical properties of the fab-
ricated microfluidic chip have been investigated to clarify
whether these reflect the reversal of the flow direction. In
accordance with the electrical measurements we propose
and evaluate an equivalent circuit diagram. Supplemen-
tary details related to the present work can be found in
Ref. [17].
II. EXPERIMENTAL
A. System design
The microchip was fabricated for studies of the basic
electrokinetic properties of the system. Hence, a simple
microfluidic circuit was designed to eliminate potential
side-effects due to complex device issues. The chip con-
sists of two 500 µm thick Pyrex glass wafers anodically
bonded together. Metal electrodes are defined on the bot-
tom wafer and channels are contained in the top wafer, as
illustrated schematically in Fig. 1(a). This construction
ensures an electrical insulated chip with fully transparent
channels.
An electrode geometry akin to the one utilized by
Brown et al. [5] and Studer et al. [10] was chosen. The
translation period of the electrode array is 50 µm with
electrode widths of W1 = 4.2 µm and W2 = 25.7 µm,
and corresponding electrode spacings of G1 = 4.5 µm
and G2 = 15.6 µm, see Fig. 1(d). Further theoretical
investigations have shown that this geometry results in
a nearly optimal flow velocity [16]. The total electrode
array consists of eight sub-arrays each having their own
connection to the shared contact pad, Fig. 1(b). This
construction makes it possible to disconnect a malfunc-
tioning sub-array. The entire electrode array has a width
of 1.3 mm ensuring that the alignment of the electrodes
and the 1.0 mm wide fluidic channels is not critical.
A narrow side channel, Fig. 1(b), allows beads to be in-
troduced into the part of the channel without electrodes,
where a number of ruler lines with a spacing of 200 µm
enable flow measurements by particle tracing, Fig. 1(c).
An outer circuit of valves and tubes is utilized to con-
http://arxiv.org/abs/0704.1321v1
FIG. 1: (a) Sketch of the fabricated chip consisting of two
Pyrex glass wafers bonded together. The channels are etched
into the top wafer, which also contains the fluid access ports.
Flow-generating electrodes are defined on the bottom wafer.
(b) Micrograph of the full chip containing a channel (white)
with flow-generating electrodes (black) and a narrow side
channel for bead injection (upper right corner). During flow
measurements the channel ends marked with an asterisk are
connected by an outer tube. The electrode array is divided
into eight sub arrays, each having its own connection to the
electrical contact pad. (c) Magnification of the framed area
in panel (b) showing the flow-generating electrodes to the left
and the measurement channel with ruler lines to the right. (d)
Close up of an electrode array section with electrode transla-
tion period of 50 µm.
trol and direct electrolytes and bead solutions through
the channels. During flow-velocity measurements, the
inlet to the narrow side channel is blocked and to elimi-
nate hydrostatic pressure differences the two ends of the
main channel are connected by an outer teflon tube with
an inner diameter of 0.5 mm. The hydraulic resistance of
this outer part of the pump loop is three orders of mag-
nitude smaller than the on-chip channel resistance and is
thus negligible.
The maximal velocity of the Poiseuille flow in the
measurement channel section is denoted vpois, and the
average slip velocity generated above the electrodes by
electroosmosis is denoted vslip. To obtain a measurable
vpois at as low applied voltages as possible, the electrode
coverage of the total channel length is made as large
Channel height H 33.6 µm
Channel width w 967 µm
Channel length Ltot 40.8 mm
Channel length with electrodes Lel 16.0 mm
Width of electrode array wel 1300 µm
Narrow electrode gap G1 4.5 µm
Wide electrode gap G2 15.6 µm
Narrow electrode width W1 4.2 µm
Wide electrode width W2 25.7 µm
Electrode thickness h 0.40 µm
Electrode surface area ([W1 + 2h]w) A1 4.84 × 10
−9 m2
Electrode surface area ([W2 + 2h]w) A2 25.63 × 10
−9 m2
Number of electrode pairs p 312
Electrode resistivity (Pt) ρ 10.6 × 10−8 Ωm
Electrolyte conductivity (0.1 mM) σ 1.43 mS/m
Electrolyte conductivity (1.0 mM) σ 13.5 mS/m
Electrolyte permittivity ǫ 80 ǫ0
Pyrex permittivity ǫp 4.6 ǫ0
TABLE I: Dimensions and parameters of the fabricated mi-
crofluidic system.
as possible. In our system the total channel length is
Ltot = 40.8 mm and the section containing electrodes
is Lel = 16.0 mm, which ensures a high Poiseuille flow
velocity, vpois = (3/4)(Lel/Ltot)vslip = 0.29 vslip [17].
The microfluidic chip has a size of approximately
16 mm × 28 mm and is shown in Fig. 1, and the device
parameters are listed in Table I.
B. Chip fabrication
The flow-generating electrodes of e-beam evaporated
Ti(10 nm)/Pt(400 nm) were defined by lift-off in 1.5 µm
thick photoresist AZ 5214-E (Hoechst) using a negative
process. The Ti layer ensures good adhesion to the Pyrex
substrate. Platinum is electrochemically stable and has
a low resistivity, which makes it suitable for the applica-
tion. By choosing an electrode thickness of h = 400 nm,
the metallic resistance between the contact pads and the
channel electrolyte is at least one order of magnitude
smaller than the resistance of the bulk electrolyte cover-
ing the electrode array.
In the top Pyrex wafer the channel of width w =
967 µm and height H = 33.6 µm was etched into the
surface using a solution of 40% hydrofluoric acid. A
100 nm thick amorphous silicon layer was sputtered onto
the wafer surface and used as etch mask in combination
with a 2.2 µm thick photoresist layer. The channel pat-
tern was defined by a photolithography process akin to
the process used for electrode definition, and the wafer
backside and edges were protected with a 70 µm thick
etch resistant PVC foil. The silicon layer was then etched
away in the channel pattern using a mixture of nitric
acid and buffered hydrofluoric acid, HNO3:BHF:H2O =
20:1:20. The wafer was subsequently baked at 120◦C to
harden the photoresist prior to the HF etching of the
channels. Since the glass etching is isotropic, the chan-
nel edges were left with a rounded shape. However, this
has only a minor impact on the flow profile, given that
the channel aspect ratio is w/H ≈ 30. The finished wafer
was first cleaned in acetone, which removes both the pho-
toresist and the PVC foil, and then in a piranha solution.
After alignment of the channel and the electrode array,
the two chip layers were anodically bonded together by
heating the ensemble to 400◦C and applying a voltage
difference of 700 V across the two wafers for 10 min.
During this bonding process, the previously deposited
amorphous Si layer served as diffusion barrier against the
sodium ions in the Pyrex glass. Finally, immersing the
chip in DI-water holes were drilled for the in- and outlet
ports using a cylindrical diamond drill with a diameter
of 0.8 mm.
C. Measurement setup and procedures
Liquid injection and electrical contact to the microchip
was established through a specially constructed PMMA
chip holder, shown in Fig. 2. Teflon tubing was fitted
into the holder in which drilled channels provided a con-
nection to the on-chip channel inlets. The interface from
the chip holder to the chip inlets was sealed by O-rings.
Electrical contact was obtained with spring loaded con-
tact pins fastened in the chip holder and pressed against
the electrode pads. The inner wires of thin coax cables
were soldered onto the pins and likewise fastened to the
holder.
The pumping was induced by electrolytic solutions
of KCl in concentrations ranging from c = 0.1 mM to
1.0 mM. The chip was prepared for an experiment by
careful injection of this electrolyte into the channel and
tubing system, after which the three valves to in- and
outlets were closed. The electrical impedance spectrum
of the microchip was measured before and after each
series of flow measurements to verify that no electrode
damaging had occurred during the experiments. If the
Top PMMA plate
Bottom PMMA plate
Contact pins
Aluminum holder
Coax cables
O-ringFitting
FIG. 2: Chip holder constructed to connect external tubing
and electrical wiring with the microfluidic chip.
impedance spectrum had changed, the chip and the se-
ries of performed measurements were discarded. Veloc-
ity measurements were only carried out when the tracer
beads were completely at rest before biasing the chip,
and it was always verified that the beads stopped mov-
ing immediately after switching off the bias. The steady
flow was measured for 10 s to 30 s. After a series of mea-
surements was completed, the system was flushed thor-
oughly with milli-Q water. When stored in milli-Q water
between experiments the chips remained functional for
at least one year.
D. AC biasing and impedance measurements
Using an impedance analyzer (HP 4194 A), electrical
impedance spectra of the microfluidic chip were obtained
by four-point measurements, where each contact pad was
probed with two contact pins. Data was acquired from
100 Hz to 15 MHz. To avoid electrode damaging by
application of a too high voltage at low frequencies, all
impedance spectra were measured at Vrms = 10 mV.
The internal sinusoidal output signal of a lock-in am-
plifier (Stanford Research SR830DSP) was used for AC
biasing of the electrode array during flow-velocity mea-
surements. The applied rms voltages were in the range
from 0.5 V to 2 V and the frequencies between 0.5 kHz
and 100 kHz. A current amplification was necessary to
maintain the correct potential difference across the elec-
trode array, since the overall chip resistance could be
small (∼ 0.1 kΩ to 1 kΩ) when frequencies in the given in-
terval were applied. The current through the microfluidic
chip was measured by feeding the output signal across a
small series resistor back into the lock-in amplifier.
The lock-in amplifier was also used for measuring
impedance spectra for frequencies below 100 Hz, which
were beyond the span of the impedance analyzer.
E. Flow velocity measurements
After filling the channel with an electrolyte and ac-
tuating the electrodes, the flow measurements were per-
formed by tracing beads suspended in the electrolyte.
Fluorescent beads (Molecular Probes, FluoSpheres F-
8765) with a diameter of 1 µm were introduced into
the measurement section of the channel and used as
flow markers for the velocity determination. A stereo
microscope was focused at the beads, and with an at-
tached camera pictures were acquired with time intervals
of ∆t = 0.125 s to 1.00 s depending on the bead velocity.
Subsequently, the velocity was determined by averaging
over a distance of ∆x = 200 µm, i.e., v = ∆x/∆t. Only
the fastest beads were used for flow detection, since these
are assumed to be located in the vertical center of the
channel. It should be noted that the use of fluorescent
particles prevented an introduction of significant illumi-
nation heating of the sample.
                    
                             
            
            
1 10 100
f [kHz]
1.0 V
1.5 V (Day 1)
1.5 V (Day 4)
1.5 V (Day 12)
FIG. 3: Reproducible flow-velocities induced in a 0.1 mM
KCl solution and observed at different days as a function of
frequency at a fixed rms voltage of 1.5 V. A corresponding
series was measured at Vrms = 1.0 V. Lines have been added
to guide the eye.
The limited number of acquired pictures led to an un-
certainty of 5% in the determination of flow velocities,
which corresponds to the movement of the tracer beads
within 0.5 to 1 frame. Additionally, there is a statistical
uncertainty on the vertical particle position in the chan-
nel, which is estimated to introduce up to 10% error on
the determined bead velocity. It is then assumed that the
fastest beads are positioned within H/3 of the maximum
of the Poiseuille flow profile.
III. RESULTS
In the parameter ranges corresponding to those pub-
lished in the literature, our flow velocity measurements
are in agreement with previously reported results. Us-
ing a c = 0.1 mM KCl solution and driving voltages
of Vrms = 1.0 V to 1.5 V over a frequency range of
f = 1.1 kHz to 100 kHz, we observed among other mea-
surement series the pumping velocities shown in Fig. 3.
The general tendencies were an increase of velocity to-
wards lower frequencies and higher voltages, and absence
of flow above f ∼ 100 kHz. The measured velocities cor-
responded to slightly more than twice those measured
by Studer et al. [10] due to our larger electrode cover-
age of the total channel. We observed damaging of the
electrodes if more than 1 V was applied to the chip at
a driving frequency below 1 kHz, for which reason there
are no measurements at these frequencies. It is, however,
plausible that the flow velocity for our chip peaked just
below f ∼ 1 kHz.
                
0.00 0.25 0.50 0.75 1.00 1.25 1.50
Vrms [V]
s] 0.1 mM
0.4 mM
0.4 mM
0.5 mM
0.5 mM
f = 1.0 kHz
f [kHz]
Vrms = 0.8 V
                
0.00 0.25 0.50 0.75 1.00 1.25 1.50
Vrms [V]
c = 0.4 mM
CsAeff
2.30 µF
2.30 µF
0.55 µF
10 30
f [kHz]
f = 1.0 kHz
f = 12.5 kHz
f = 21.0 kHz
Vrms = 0.8 V
FIG. 4: (a) Reversed flow observed for repeated measure-
ments of two concentrations of KCl at 1.0 kHz. The inset
shows that for a 0.4 mM KCl solution at a fixed rms volt-
age of 0.8 V the flow direction remains negative, but slowly
approaches zero for frequencies up to 50 kHz. (b) The theo-
retical model presented in Ref. [19] predicts the trends of the
experimentally observed velocity curves. The depicted graphs
are calculated for a c = 0.4 mM solution and parameters cor-
responding to the experiments (Table III) with ζeq = 160 mV.
Additional curves have been plotted for slightly different pa-
rameter values in order to obtain a closer resemblance to the
experimental graphs, see Sec. IV.
A. Reproducibility of measurements
Our measured flow velocities were very reproducible
due to the employed MEMS chip fabrication techniques
and the careful measurement procedures described in
Sec. II. This is illustrated in Fig. 3, which shows three
velocity series recorded several days apart. The mea-
surements were performed on the same chip and for the
same parameter values. Between each series of measure-
ments, the chip was dismounted and other experiments
                      
                      
0.1 1 10 102 103 104 105 106 107 108
f [Hz]
|Z| (meas)
|Z| (fit)
θ (meas)
θ (fit)
|Z| ✲θ✛
FIG. 5: Bode plot showing the measured amplitude |Z|
(right ordinate axis) and phase θ (left ordinate axis) of the
impedance as a function of frequency over eight decades from
0.2 Hz to 15 MHz. The voltage was Vrms = 10 mV and the
electrolyte concentration c = 1.0 mM KCl. The measure-
ments are shown with symbols while the curves of the fitted
equivalent diagram are represented by dashed lines. The mea-
surement series obtained with the Impedance Analyzer consist
of 400 very dense points while the series measured using the
lock-in amplifier contains fewer points with a clear spacing.
performed. However, it should be noted that a very slow
electrode degradation was observed when a dozen of mea-
surement series were performed on the same chip over a
couple of weeks.
B. Low frequency reversed flow
Devoting special attention to the low-frequency (f <
20 kHz), low-voltage regime (Vrms < 2 V), not studied
in detail previously, we observed an unanticipated flow
reversal for certain parameter combinations. Fig. 4(a)
shows flow velocities measured for a frequency of 1.0 kHz
as a function of applied voltage for various electrolyte
concentrations. It is clearly seen that the velocity series
of c = 0.1 mM exhibits the known exclusively forward
and increasing pumping velocity as function of voltage,
whereas for slightly increased electrolyte concentrations
an unambiguous reversal of the flow direction is observed
for rms voltages below approximately 1 V.
This reversed flow direction was observed for all fre-
quencies in the investigated spectrum when the elec-
trolyte concentration and the rms voltage were kept con-
stant. This is shown in the inset of Fig. 4(a), where a
velocity series was obtained over the frequency spectrum
for an electrolyte concentration of 0.4 mM at a constant
rms voltage of 0.8 V. It is noted that the velocity is nearly
constant over the entire frequency range and tends to zero
above f ∼ 20 kHz.
✻log |Z|
log(ω)
Rb Rel
(a) (b)
FIG. 6: (a) Equivalent circuit diagram. (b) Sketch of the
impedance amplitude curve of the equivalent diagram. It con-
sists of three plateaus, and four characteristic frequencies ωx,
ω0, ωD and ωel (see Table II) that characterize the shape and
may be utilized to estimate the component values.
C. Electrical characterization
To investigate whether the flow reversal was connected
to unusual properties of the electrical circuit, we care-
fully measured the impedance spectrum Z(f) of the mi-
crofluidic system. Spectra were obtained for the chip
containing KCl electrolytes with the different concentra-
tions c = 0.1 mM, 0.4 mM and 1.0 mM.
Fig. 5 shows the Bode plots of the impedance spec-
trum obtained for c = 1.0 mM. For frequencies between
f ∼ 1 Hz and f ∼ 103 Hz the curve shape of the
impedance amplitude |Z| is linear with slope −1, after
which a horizontal curve section follows, and finally the
slope again becomes−1 for frequencies above f ∼ 106 Hz.
Correspondingly, the phase θ changes between 0◦ and
90◦. From the decrease in phase towards low frequen-
cies it is apparent that |Z| must have another horizontal
curve section below f ∼ 1 Hz. When the curve is hori-
zontal and the phase is 0◦ the system behaves resistively,
while it is capacitively dominated when the phase is 90◦
and the curve has a slope of −1.
Debye length λD
Total electrode resistance Rel
Total bulk electrolyte resistance Rb
Total faradaic (charge transfer) resistance Rct
Internal resistance in lock-in amplifier R
Total measured resistance for ω → 0 Rx
Total electrode capacitance Cel
Total double layer capacitance Cdl
Debye layer capacitance CD
Surface capacitance Cs
Debye frequency ωD
Inverse ohmic relaxation time ω0
Inverse faradaic charge transfer time (primarily) ωx
Characteristic frequency of electrode circuit ωel
TABLE II: List of the symbols used in the equivalent circuit
model.
Rb Rb Rel Rel Rct Cdl Cdl Cel Cel ωD ωD ω0 ω0
mod meas mod meas meas mod meas mod meas mod meas mod meas
[kΩ] [kΩ] [Ω] [Ω] [MΩ] [µF] [µF] [nF] [nF] [M rad s−1] [k rad s−1]
0.1 mM (A) 2.0 1.0 7.6 5 1.0 0.50 0.50 0.28 0.30 2.0 3.3 1.0 2.0
1.0 mM (A) 0.21 0.17 7.6 6 1.0 0.56 0.55 0.28 0.29 19.1 20.6 8.5 10.7
0.1 mM (B) 2.0 1.4 7.6 6 − 0.50 0.51 0.28 0.29 2.0 3.0 1.0 1.4
0.4 mM (B) 0.52 0.41 7.6 7 − 0.54 0.53 0.28 0.28 7.7 9.3 3.6 4.6
1.0 mM (B) 0.21 0.17 7.6 8 − 0.56 0.55 0.28 0.26 19.1 22.6 8.5 10.5
TABLE III: Comparison of measured (meas) and modeled (mod) values of the components in the equivalent diagram, Fig. 6.
The measured values are given by curve fits of Bode plots, Fig. 5, obtained on two similar chips labeled A and B, respectively.
The modeled values are estimated on basis of Table I and a particular choice of the parameters ζeq and Cs. This choice is not
unique since different combinations can lead to the same value of Cdl.
D. Equivalent circuit
In electrochemistry the standard way of analyzing such
impedance measurements is in terms of an equivalent
circuit diagram [20]. The choice of diagram is not un-
ambiguous [3]. We have chosen the diagram shown in
Fig. 6(a) with the component labeling listed in Table II.
Charge transport through the bulk electrolyte is repre-
sented by an ohmic resistance Rb, accumulation of charge
in the double layer at the electrodes by a capacitance Cdl,
and faradaic current injection from electrochemical reac-
tions at the electrodes by another resistance, the charge-
transfer resistance Rct [16, 20]. Moreover, we include the
ohmic resistance of the metal electrodes Rel, the mutual
capacitance between the narrow and wide electrodes Cel,
and a shunt resistance R
′ = 10 MΩ to represent the
internal resistance of the lock-in amplifier.
Finally, in electrochemical experiments at low fre-
quency, the electrical current is often limited by diffusive
transport of the reactants in the faradaic electrode reac-
tion to and from the electrodes. This can be modeled
by adding a frequency dependent Warburg impedance
in series with the charge transfer resistance [20]. How-
ever, because the separation between the electrodes is so
small and the charge transfer resistance is so large, we
are unable to distinguish the Warburg impedance in the
impedance measurements and leave it out of the equiva-
lent diagram.
By fitting the circuit model to the impedance mea-
surements we extract the component values listed in Ta-
ble III. On the chip labeled B we were unable to measure
the charge transfer resistance due to a minor error on the
chip introduced during the bonding process. Fig. 6(b) il-
lustrates the relation between component values and the
impedance amplitude curve through four characteristic
angular frequencies ω = 2πf . The inverse frequency
Cdl primarily expresses the characteristic time
for the faradaic charge transfer into the Debye layer. The
characteristic time for charging the Debye layer through
the electrolyte is given by ω−10 = Rb Cdl. The Debye fre-
quency is ωD = 1/(RbCel), and finally ωel = 1/(RelCel)
simply states the characteristic frequency for the on-chip
electrode circuit in the absence of electrolyte. It is noted
that the total DC-limit resistance R
corresponds to the
parallel coupling between R
′ and Rct.
IV. DISCUSSION
In the following we investigate to which extent the gen-
eral theory of induced-charge (AC) electroosmosis can ex-
plain our observations and experimental data. We first
use the equivalent circuit component values extracted
from the impedance measurements to estimate some im-
portant electrokinetic parameters based on the Gouy–
Chapman–Stern model [20], namely, the Stern layer ca-
pacitance Cs, the intrinsic zeta potential ζeq on the elec-
trodes and the charge transfer resistance Rct. Then
we use this as input to the weakly nonlinear electro-
hydrodynamic model presented in Ref. [19], which is an
extension of the model in Ref. [16]. We compare theoret-
ical values with experimental observations, and discuss
the experimentally observed trends of the flow velocities.
A. Impedance analysis
The impedance measurements are performed at a low
voltage of Vrms = 10 mV so it might be expected that
Debye–Hückel linear theory applies (V . 25 mV). How-
ever, since we only measure the potential difference be-
tween the electrodes and we do not know the potential of
the bulk electrolyte, we cannot say much about the exact
potential drop across the double layer. Many electrode-
electrolyte systems posses an intrinsic zeta potential at
equilibrium ζeq of up to a few hundred mV. Indeed, the
measured Cdl is roughly 10 times larger than predicted by
Debye–Hückel theory, which indicates that the intrinsic
zeta potential is at least ±125 mV.
According to Gouy–Chapman–Stern theory the Cdl
can be expressed as a series coupling of the compact Stern
layer capacitance Cs and the differential Debye-layer ca-
pacitance CD,
, (1)
where the two double-layer capacitances of an elec-
trode pair are coupled in series through the electrolyte,
and since the p electrode pairs are coupled in parallel,
the effective area of the total double layer is Aeff =
pA1A2/(A1+A2). A1 and A2 are the total surface areas
exposed to the electrolyte of a narrow and wide electrode,
respectively. For simplicity Cs is often assumed constant
and independent of potential and concentration, while
CD is given by the Gouy–Chapman theory as
ζeqze
. (2)
Unfortunately, it is not possible to estimate the exact
values of both Cs and ζeq from a measurement of Cdl,
because a range of parameters lead to the same Cdl. We
can, nevertheless, state lower limits as Cs ≥ 0.39 F/m
and |ζeq| ≥ 175 mV for c = 0.1 mM or Cs ≥ 0.43 F/m
and |ζeq| ≥ 125 mV at c = 1.0 mM.
For the model values in Table III we used Eq. (1) with
Cs = 1.8 F/m
2 and ζeq = 190 mV, 160 mV and 140 mV
at 0.1 mM, 0.4 mM and 1.0 mM KCl, respectively, in ac-
cordance with the trend often observed that ζeq decreases
with increasing concentration, [21]. The bulk electrolyte
resistance can be expressed as
, (3)
where σ is the conductivity, w is the width of the elec-
trodes and p is the number of electrode pairs, see Table I,
and 0.85 is a numerical factor computed for our particular
electrode layout using the finite-element based program
Comsol Multiphysics. Similarly, the mutual capaci-
tance between the electrodes can be calculated as
Cel =
ǫw + ǫp(2wel − w)
, (4)
and the resistance Rel of the electrodes leading from the
contact pads to the array is simply estimated from the
resistivity of platinum and the electrode geometry.
At frequencies above 100 kHz the impedance is dom-
inated by Rb, Cel and Rel, and the Bode plot closely
resembles a circuit with ideal components, see Fig. 5.
Around 1 kHz we observe some frequency dispersion
which could be due to the change in electric field line
pattern around the inverse RC-time ω0 = 1/(RbCdl) [19].
Finally, below 1 kHz where the impedance is dominated
by Cdl, the phase never reaches 90
◦ indicating that the
double layer capacitance does not behave as an ideal ca-
pacitor but more like a constant phase element (CPE).
This behavior is well known experimentally, but not fully
understood theoretically [22].
B. Flow
The forward flow velocities measured at c = 0.1 mM as
a function of frequency, Fig. 3, qualitatively exhibit the
trends predicted by standard theory, namely, the pump-
ing increases with voltage and falls off at high frequency
[4, 14].
More specifically, the theory predicts that the pumping
velocity should peak at a frequency around the inverse
RC-time ω0, corresponding to f ≈ 0.3 kHz, and decay as
the inverse of the frequency for our applied driving volt-
ages, see Fig. 11 in Ref. [16]. Furthermore, the velocity
is predicted to grow like the square of the driving volt-
age at low voltages, changing to V log V at large voltages
[16, 19].
Experimentally, the velocity is indeed proportional to
ω−1 and the peak is not observed within the range
1.1 kHz to 100 kHz, but it is likely to be just below
1 kHz. However, the increase in velocity between 1.0 V
and 1.5 V displayed in Fig. 3 is much faster than V 2.
That is also the result in Fig. 4(a) for c = 0.1 mM where
no flow is observed below Vrms = 0.5 V, while above that
voltage the velocity increases rapidly. For c = 0.4 mM
and c = 0.5 mM the velocity even becomes negative at
voltages Vrms ≤ 1 V. This cannot be explained by the
standard theory and is also rather different from the re-
verse flow that has been observed by other groups at
larger voltages Vrms > 2 V and at frequencies above the
inverse RC-time [10, 12, 13].
The velocity shown in the inset of Fig. 4(a) is re-
markable because it is almost constant between 1 kHz
and 10 kHz. This is unlike the usual behavior for AC
electroosmosis that always peaks around the inverse RC-
time, because it depends on partial screening at the elec-
trodes to simultaneously get charge and tangential field
in the Debye layer. At lower frequency the screening is
almost complete so there is no electric field in the elec-
trolyte to drive the electroosmotic fluid motion, while at
higher frequency the screening is negligible so there is no
charge in the Debye layer and again no electroosmosis.
One possible explanation for the almost constant veloc-
ity as a function of frequency could be that the amount of
charge in the Debye layer is controlled by a faradaic elec-
trode reaction rather than by the ohmic current running
through the bulk electrolyte. Our impedance measure-
ment clearly shows that the electrode reaction is negli-
gible at f = 1 kHz and Vrms = 10 mV bias, but since
the reaction rate grows exponentially with voltage in an
Arrhenius type dependence, it may still play a role at
Vrms = 0.8 V. However, previous theoretical investiga-
tions have shown that faradaic electrode reactions do not
lead to reversal of the AC electroosmotic flow or pumping
direction [16].
Due to the strong nonlinearity of the electrode reaction
and the asymmetry of the electrode array, there may also
be a DC faradaic current running although we drive the
system with a harmonic AC voltage. In the presence of
an intrinsic zeta potential ζeq on the electrodes and/or
the glass substrate this would give rise to an ordinary
DC electroosmotic flow. This process does not necessar-
ily generate bubbles because the net reaction products
from one electrode can diffuse rapidly across the narrow
electrode gap to the opposite electrode and be consumed
by the reverse reaction.
To investigate to which extent this proposition ap-
plies, we used the weakly nonlinear theoretical model pre-
sented in [19]. The model extends the standard model for
AC electroosmosis by using the Gouy–Chapman–Stern
model to describe the double layer, and Butler–Volmer
reaction kinetics to model a generic faradaic electrode
reaction [20]. The concentration of the oxidized and re-
duced species in the diffusion layer near the electrodes is
modeled by a generalization of the Warburg impedance,
while the bulk concentration is assumed uniform, see
Ref. [19] for details.
The model parameters are chosen in accordance with
the result of the impedance analysis, i.e., Cs = 1.8 F/m
Rct = 1 MΩ, ζeq = 160 mV, as discussed in Sec. IVA.
Further we assume an intrinsic zeta potential of ζeq =
−100 mV on the borosilicate glass walls [21], and
choose (arbitrarily) an equilibrium bulk concentration of
0.02 mM for both the oxidized and the reduced species in
the electrode reaction, which is much less than the KCl
electrolyte concentration of c = 0.4 mM.
The result of the model calculation is shown in
Fig. 4(b). At 1 kHz the fluid motion is dominated by
AC electroosmosis which is solely in the forward direc-
tion. However, at 12.5 kHz the AC electroosmosis is
much weaker and the model predicts a (small) reverse
flow due to the DC electroosmosis for Vrms < 1 V.
Fig. 4(b) shows that the frequency interval with reverse
flow is only from 30 kHz down to 10 kHz, while the mea-
sured velocities remain negative down to at least 1 kHz.
The figure also shows results obtained with a lower Stern
layer capacitance Cs = 0.43 F/m
2 in the model, which
turns out to enhance the reverse flow.
In both cases, the reverse flow predicted by the theoret-
ical model is weaker than that observed experimentally
and does not show the almost constant reverse flow pro-
file below 10 kHz. Moreover, the model is unable to ac-
count for the strong concentration dependence displayed
in Fig. 4(a).
According to Ref. [18], steric effects give rise to a sig-
nificantly lowered Debye layer capacitance and a poten-
tially stronger concentration dependence when ζ exceeds
10 kBT/e ∼ 250 mV, which roughly corresponds to a
driving voltage of Vrms ∼ 0.5 V. Thus, by disregarding
these effects we overestimate the double layer capacitance
slightly in the calculations of the theoretical flow velocity
for Vrms = 0.8 V. This seems to fit with the observed ten-
dencies, where theoretical velocity curves calculated on
the basis of a lowered Cdl better resemble the measured
curves.
Finally, it should be noted that several electrode reac-
tions are possible for the present system. As an example
we mention 2H2O(l) +O2(aq) + 4e
− ⇋ 4OH−
. This re-
action is limited by the amount of oxygen present in the
solution, which in our experiment is not controlled. If
this reaction were dominating the faradaic charge trans-
fer, the value of Rct could change from one measurement
series to another.
V. CONCLUSION
We have produced an integrated AC electrokinetic mi-
cropump using MEMS fabrication techniques. The re-
sulting systems are very robust and may preserve their
functionality over years. Due to careful measurement
procedures it has been possible over weeks to reproduce
flow velocities within the inherent uncertainties of the
velocity determination.
An hitherto unobserved reversal of the pumping direc-
tion has been measured in a regime, where the applied
voltage is low (Vrms < 1.5 V) and the frequency is low
(f < 20 kHz) compared to earlier investigated parameter
ranges. This reversal depends on the exact electrolytic
concentration and the applied voltage. The measured
velocities are of the order −5 µm/s to −10 µm/s. Previ-
ously reported studies of flow measured at the same pa-
rameter combinations show zero velocity in this regime
[10]. The reason why we are able to detect the flow
reversal is probably our design with a large electrode
coverage of the channel leading to a relative high ratio
vpois/vslip = 0.29.
Finally, we have performed an impedance character-
ization of the pumping devices over eight frequency
decades. By fitting Bode plots of the data, the measured
impedance spectra compared favorably with our model
using reasonable parameter values.
The trends of our flow velocity measurements are ac-
counted for by a previously published theoretical model,
but the quantitative agreement is lacking. Most impor-
tant, the predicted velocities do not depend on electrolyte
concentration, yet the concentration seems to be one of
the causes of our measured flow reversal, Fig. 4(a). This
shows that there is a need for further theoretical work on
the electro-hydrodynamics of these systems and in partic-
ular on the effects of electrolyte concentration variation.
Acknowledgments
We would like to thank Torben Jacobsen, Department
of Chemistry (DTU), for enlightening discussions about
electrokinetics and the interpretation of impedance mea-
surements on electrokinetic systems.
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