Microfluidic actuation by modulation of surface stresses

TL;DR: In this paper, the authors demonstrate the active manipulation of nanoliter liquid samples on the surface of a glass or silicon substrate by combining chemical surface patterning with electronically addressable microheater arrays.

Abstract: We demonstrate the active manipulation of nanoliter liquid samples on the surface of a glass or silicon substrate by combining chemical surface patterning with electronically addressable microheater arrays. Hydrophilic lanes designate the possible routes for liquid migration while activation of specific heater elements determine the trajectories. The induced temperature fields spatially modulate the liquid surface tension thereby providing electronic control over the direction, timing, and flow rate of continuous streams or discrete drops. Temperature maps can be programed to move, split, trap, and mix ultrasmall volumes without mechanically moving parts and with low operating voltages of 2–3 V. This method of fluidic actuation allows direct accessibility to liquid samples for handling and diagnostic purposes and provides an attractive platform for palm-sized and battery-powered analysis and synthesis.

Summary

Introduction

• SINCE THE eighties, the resonance method to improve thegain of printed antennas has been well documented [1]–[3].
• Frequency selective surfaces (FSS) [13] based on the Fabry-Perot effect [14] have also been proposed as an alternative to dielectric EBGs for gain enhancement.
• The distance between the FSS superstrate and the ground plane of the antenna, which determines the resonant frequency, still needs to be about of the resonant frequency of the resonator.

II. META-SURFACE DESIGN

• During the recent years, several double negative materials (DNG) have been designed by different authors [23]–[25] several of them based on the topology proposed by [26], i.e., a combination of split ring resonators (SRRs) and wires.
• The meta-surface under study is based on the unit cell proposed by Prof. Ziolkowski in [25].
• The material selected to fabricate the layers was RT/Duroid 5880, a low loss dielectric characterized by the parameters , loss tangent , thickness 0.254 mm and copper cladding 70 on both faces.
• The transmission and reflection properties of the manufactured meta-surface were tested under waveguide excitation.
• The measured results are depicted in Fig.

III. RADIATION PERFORMANCE

• As was mentioned before, this meta-surface is basically a resonant structure exhibiting pass and stop bands.
• It is formed by a finite periodic repetition of the unit cell.
• By tuning a dipole antenna to the pass band frequency of the superstrate, an in-phase resonance of the unit cells will be induced leading to a more uniform illumination of the superstrate.
• The dimensions and position of the dipole were optimized by simulating it embedded in a dielectric slab of and loaded with the superstrate.
• Fig. 4 shows the deviation of the resonant frequency of the dipole with and without superstrate with respect to the optimized configuration when the dimensions of the dipole are slightly modified.

A. Parameter

• The parameter of the dipole with the superstrate was measured by using a network analyzer (Marconi 6210 Reflection Analyzer).
• Based on the simulation optimization process the dipole was placed just above the superstrate.
• The set-up for the measurements is shown in Fig.
• The influence of the meta-surface in the impedance matching of the dipole was analyzed and measured by varying the number of periods of the superstrate in the x direction from 4 to 12.
• As expected, an impedance matching better than 12 dB with a resonant frequency around 11.1 GHz and a deviation smaller than 3.5% with respect to the central frequency has been obtained.

B. Resonant Frequency

• Fig. 7 shows the dependence of the resonant frequency (minimum ) of the configuration (meta-surface + dipole) and the frequency of maximum gain at boresight with the number of cells of the superstrate.
• The process of deriving the gain will be explained in the next section.
• It can be observed that both parameters do not exactly coincide, but there is a slight frequency shift between them.
• A similar tendency was obtained in both cases; as the number of cells increases, the resonant frequency decreases varying from 11.19 GHz in the case of 4 cells to 10.9 GHz in the case of 12 cells [this agrees with the result obtained with the waveguide measurements (see Fig. 2)].
• The resonant frequency curve flattens for larger superstrates since the meta-surface trends to behave as a more uniform media resonating at 10.9 GHz instead of a set of single scatterers.

C. Gain

• In order to characterize the different configurations in terms of absolute-gain, the two-antenna method described in [27] was followed.
• The gain of the radiating configurations was measured in an anechoic chamber and compared with the one of a single dipole by using a horn antenna as receiver and the dipole (with and without superstrate) as transmitter.
• The superstrate was placed close to the dipole, as in the case of the measurements, in order to maximize the power radiated at boresight.
• The set-up used for these measurements is shown in Fig.
• The reason for this is the appearance of a standing wave in the transversal direction of the configuration, which limits the maximum size of the structure that achieves large gain.

D. Radiation Pattern

• Once the frequency of maximum gain was known (see Fig. 9), the radiation patterns were measured at that frequency.
• In order to avoid reflections from the clamp and the feeding cable, the back side of the antenna was covered with the absorbing material shown in Fig. 8(b).
• The back radiation pattern (from 90 to 270 ) was not measured because of physical limitations in the test set-up (see the back side feeding network and clamp in Fig. 8).
• Fig. 11 shows the H and E-plane radiation patterns for the case of nine cells.
• The back radiation level at 180 was around 5 dB what means a front-back radiation of 10 dB.

E. Radiation Efficiency

• The radiation efficiency is defined as the ratio of the total power radiated by the antenna to the total power accepted by the antenna at its terminals during radiation.
• Following this approach, the radiation efficiency has been computed for all the configurations, (see Fig. 13 solid line), taking into account 1 dB errors in the gain measurements.
• For superstrates smaller or larger, the radiation efficiency reduces, but it always exceeds 50%.
• So, the real part of the input impedance with the sphere in place will be .
• Thus by making two impedance measurements, without and with the cap, the radiation efficiency can be determined by using (5).

F. Effective Area

• Once the maximum directivity at boresight of the configuration is obtained, the effective area of the meta-surface can be calculated by applying (6) (6) Fig. 14 shows a comparison between the effective area derived from the measurements (taking into account the errors in the measurements of the gain) and the physical area of the meta-surface.
• When the superstrate is small (4 unit cells; equal to ), it can be observed that the effective area is larger than the physical one.
• This is an artefact effect produced by the mathematical definition of the effective area when the radiating surface is not wide enough and there are not metallic walls surrounding the antenna.
• This is a known phenomena described by Balanis for dipole antennas [27] p. 83.
• For larger superstrates (from five to eight cells), the effective area is similar to the physical one, what means that the meta-surface is completely illuminated, i.e., a uniform illumination has been achieved.

IV. MULTIFREQUENCY ANTENNA CONFIGURATION

• The results obtained in the previous sections show that the physical area of the proposed structure can be used very effectively in order to enhance the radiation performance of planar antennas due to the uniform illumination of the superstrate.
• It is possible to place the same type of unit cell but with a different resonant frequency (same shape but different size) on both sides.
• In order to implement it, the unit cell explained in Section II has been scaled to be working at a higher frequency, around 12.5 GHz.
• By combining superstrates consisting of low resonant frequency (LRF) unit cells and high resonant frequency (HRF) ones, and tuning dipoles to these frequencies, the MFAA is designed.
• The MFAA studied is schematically depicted in Fig. 16.

V. CONCLUSION

• A novel implementation to enhance the radiation performances of a dipole antenna based on the use of meta-surfaces as superstrate has been presented.
• A finite uniform meta-surface has been characterized in terms of parameter, gain, radiation pattern, radiation efficiency and effective area.
• Measurements of different configurations have proven an enhancement of the gain at boresight of about 3.5 1 dB with a reduction of the H-plane endfire radiation of about 15 dB.
• For larger superstrates, the effective area does not increase since the maximum area that the dipole can illuminate has been estimated around .
• Based on this configuration, a compact multifrequency antenna array has been simulated, showing the gain enhancement and low coupling between elements.

Figures

FIG. 4. ~a!–~e! Thermally induced splitting of a dodecane drop on a p tially wetting stripe (w51000mm). The voltage applied to the microheat ~155V! was 2.5 V. The images were recorded att50, 6.0, 7.5, 8.0, and 8.5 s. ~f!–~i! Dodecane drop propelled through an intersection outlined by dark gray pattern (w51000mm, time lapse 104 s!. ~j!–~l! Dodecane drop turning a 90° corner~time lapse 164 s!.

FIG. 3. ~a!–~c! Mixing of two liquids ~black and white! by thermocapillary convection induced by a transverse temperature gradient. The stripe is mm wide, h0520 mm, dT/dy54 °C/mm, andm520 mPa s. The curves shown in ~b! represent the streamlines of the convective flow.~d! Experimental positions@x(t),y(t)# of 5-mm-diam tracer particles in a rivulet flowing at a 45° angle from the direction of¹T (w5530mm and m 518 mPa s). The time increment between subsequent data points iDt 56 s. The gray band signifies a portion of the slanted hydrophilic strip

FIG. 2. Front speed of continuous streams.~a! Position dependence for fou temperature gradients on a 500-mm-wide stripe. Symbols: experimenta data; solid lines: simulations. The film thickness at the stripe inlet w treated as a fitting parameter (h054062 mm). ~b! Dependence onw for four thermal gradients.~c! Dependence ondT/dx for w5300mm.

Full text

Microfluidic actuation by modulation of surface stresses
Anton A. Darhuber, Joseph P. Valentino, Jeffrey M. Davis, and Sandra M. Troian
a)
Microfluidic Research and Engineering Laboratory, Department of Chemical Engineering,
Princeton University, Princeton, New Jersey 08544
Sigurd Wagner
Department of Electrical Engineering, Princeton University, Princeton, New Jersey 08544
共Received 26 June 2002; accepted 21 November 2002兲
We demonstrate the active manipulation of nanoliter liquid samples on the surface of a glass or
silicon substrate by combining chemical surface patterning with electronically addressable
microheater arrays. Hydrophilic lanes designate the possible routes for liquid migration while
activation of specific heater elements determines the trajectories. The induced temperature fields
spatially modulate the liquid surface tension thereby providing electronic control over the direction,
timing, and flow rate of continuous streams or discrete drops. Temperature maps can be programed
to move, split, trap, and mix ultrasmall volumes without mechanically moving parts and with low
operating voltages of 2–3 V. This method of fluidic actuation allows direct accessibility to liquid
samples for handling and diagnostic purposes and provides an attractive platform for palm-sized and
battery-powered analysis and synthesis. © 2003 American Institute of Physics.
关DOI: 10.1063/1.1537512兴
Miniaturized automated systems for liquid routing, mix-
ing, analysis, and synthesis are rapidly expanding diagnostic
capabilities in medicine, genomic research, and material
science.
1
Liquid flow in microchannels can be regulated by
pressure gradients,
2
thermocapillary pumping,
3
electrokinetic
forces,
4,5
or magnetohydrodynamic pumping.
6,7
Electrowetting
8,9
and dielectrophoresis
10
have also been used
to move droplets on an open surface. These techniques typi-
cally require high operating voltage and high electrolyte con-
centrations. We demonstrate a different method for liquid
handling and transport that uses programmable surface tem-
perature distributions, in conjunction with chemical substrate
patterning, to provide electronic control over the direction,
timing, and flow rate. This method capitalizes on the large
surface-to-volume ratio inherent in microscale systems since
the gas–liquid and liquid–solid surface energies are modu-
lated to induce and confine flow. It works equally well with
polar or nonpolar liquids, requires no mechanically moving
parts and operates at very low voltages. The open architec-
ture is best suited to liquids of low volatility. Encapsulation
schemes that retain the free liquid–air interfaces can mini-
mize evaporative loss.
Local heating of a liquid film at a position x reduces the
surface tension
␥
(x) to produce a thermocapillary shear
stress
␶
˜
•nˆ ⫽ “
␥
⫽ (
⳵
␥
/
⳵
T)“ T that pulls liquid toward re-
gions of cooler surface temperature T.
11–13
Since
⳵
␥
/
⳵
T is
essentially temperature independent for all liquids, the driv-
ing force and flow direction are proportional to “ T. For a
thin flat liquid layer, the average flow speed and flow rate
共per unit width兲 are given by
␯
(x)⫽ h(x,t)
␶
˜
•nˆ /2
␮
(x) and
Q(x,t)⫽ h(x,t)
␯
(x,t), where h(x,t) is the film thickness
and
␮
(x) the local viscosity. This phenomenon forms the
basis of our microfluidic device for actuating continuous
streams and discrete droplets.
The sample layout
14
for driving continuous streams is
shown in Fig. 1共a兲. Hydrophilic stripes connect pairs of 4.5-
mm-wide square reservoir pads; the gray areas are chemi-
cally treated to repel the liquid.
15,16
A constant temperature
gradient dT/dx is generated by an embedded heating resistor
共vertical black line兲 on the left and a cooling block 共dotted
rectangle兲 on the right. Figure 1共b兲 depicts a microstream
emerging from a reservoir into a hydrophilic stripe subject to
a streamwise temperature gradient. The liquids used were
polydimethyl-siloxane 共PDMS,
␮
⫽ 5 and 20 mPa s,
␥
⫽ 20.6 mN/m, and d
␥
/dT⫽⫺0.060 mN/m °C at 25 °C兲 and
dodecane (
␮
⫽ 1.35 mPa s,
␥
⫽ 25.5 mN/m, and d
␥
/dT
⫽⫺0.091 mN/m °C at 25 °C兲.
The speed of a continuous microstream depends on its
length L, channelwidth w, dT/dx, and the deposited volume
V
s
. We have obtained a flow speed of 600
␮
m/s for PDMS
(
␮
⫽ 5mPasat25°C兲 with dT/dx⫽ 1.44 °C/mm, w
⫽ 800
␮
m, and V
s
⫽ 8
␮
l. Flow speeds higher than 1 mm/s
can be obtained with smaller
␮
, larger
⳵
␥
/
⳵
T, and narrower,
continuously fed reservoirs. Figure 2共a兲 shows the position
a兲
Author to whom correspondence should be addressed; electronic mail:
stroian@princeton.edu
FIG. 1. 共a兲 Layout of a chemically patterned silicon sample with uniform
temperature gradient used for moving continuous streams. Gray areas are
hydrophobic, white areas hydrophilic. Liquid 共2–8
␮
l兲 deposited on a
diamond-shaped reservoir pad is propelled on a microstripe 共width 100–800
␮
m兲 due to the thermocapillary stress. The black rectangles are electrical
contact pads connecting to the subsurface heating resistor 共black line兲.The
dashed rectangle denotes the cooling block. 共b兲 Top-view optical micrograph
of a rivulet moving on a 300-
␮
m-wide channel.
APPLIED PHYSICS LETTERS VOLUME 82, NUMBER 4 27 JANUARY 2003
6570003-6951/2003/82(4)/657/3/$20.00 © 2003 American Institute of Physics
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dependence of the front speed for PDMS (
␮
⫽ 20 mPa s) and
four different gradients. The solid lines represent numerical
simulations of the front speed obtained from a lubrication
equation for the evolution of centerline film thickness h(x,t)
according to
h
t
⫹
冋
2
␶
h
2
5
␮
⫹
64h
3
315
␮
共
␥
h
xx
兲
x
⫺
192h
3
105
␮
w
2
共
␥
h
兲
x
册
x
⫽ 0, 共1兲
where subscripts denote partial differentiation. The film
shape and speed are determined by the thermocapillary driv-
ing stress 共term 2兲, capillary forces due to streamwise and
lateral surface curvature 共terms 3 and 4兲, and the
temperature-dependent viscosity.
15
The agreement with ex-
periment is excellent. The observed decrease in speed shown
in Fig. 2共a兲 is caused by the decrease in capillary forces
16
and the increase in viscosity with distance. The relevant di-
mensionless numbers 共based on parameter values at the inlet
x⫽0兲 are (l/w)
2
, where l⫽ (
␥
h
3
/3
␮
v
)
1/3
is the dynamic cap-
illary length,
17
and
␶
/p
0
where p
0
is the reservoir pressure.
15
For
兩
␶
兩
/p
0
Ⰶ 1, the inlet film height h
0
is controlled by p
0
,
which is essentially proportional to V
s
.
16
A scaling
analysis
15
then gives
␯
⬃w
2
␶
V
s
/
␮
. In the opposite limit
兩
␶
兩
/p
0
Ⰷ 1,
␶
determines the inlet height
15
and the front speed
scales as
␯
⬃(w
␶
)
3/2
/
␮
. Figure 2共b兲 shows experimental data
and least-square fits for the front speed as a function of w at
x⫽ 18 mm. To a good approximation, the data follow a
power law
␯
⬃w
␣
, where the exponents
␣
confirm the trend
from 2 to 3/2. The dependence of the front speed on dT/dx
shown in Fig. 2共c兲 also follows the scaling predictions
v
⬃
␶
␤
, where
␤
⫽ 1 and 1.47. The two data sets illustrate the
transition from reservoir to shear-dominated regimes. For in-
termediate values of
兩
␶
兩
/p
0
, the flow speed does not conform
to power laws but can only be determined by full numerical
simulations.
15
Mixing poses a difficulty in microfluidic devices due to
the absence of turbulent convection. Figures 3共a兲–3共c兲 depict
computed convection patterns obtained with a purely trans-
verse thermal gradient dT/dy in the absence of diffusion.
The interfacial area A(t) between the two liquids increases at
an essentially constant rate by a factor of 150 in just 30 s.
Simulations including molecular diffusion with coefficient
D⫽ 10
⫺ 12
m
2
/s show a reduction in the mixing time t
mix
by
three orders of magnitude compared to purely diffusive mix-
ing. The presence of both convection and diffusion leads to a
nonmonotonic scaling of t
mix
with D similar to Taylor–Aris
dispersion.
18–20
Since thermocapillary flow is proportional to
h(x,t), even faster mixing can be obtained by directing the
flow onto a wider hydrophilic patch that supports thicker
films. By imposing an additional thermal gradient dT/dx
parallel to the microstripe, the streamlines follow helical
paths thereby significantly increasing the interfacial area be-
tween merging streams. Figure 3共d兲 presents experimental
flow patterns on a hydrophilic stripe inclined by 45° to the
direction of the thermal gradient. The solid symbols desig-
nate the measured trajectories
关
x(t),y(t)
兴
of tracer particles
convected with the flow. A larger spacing between subse-
quent points signifies a faster flow near the air–liquid
interface—a smaller spacing indicates slower flow near the
solid substrate.
The resistor and channel layout used for actuation of
FIG. 2. Front speed of continuous streams. 共a兲 Position dependence for four
temperature gradients on a 500-
␮
m-wide stripe. Symbols: experimental
data; solid lines: simulations. The film thickness at the stripe inlet was
treated as a fitting parameter (h
0
⫽ 40⫾2
␮
m). 共b兲 Dependence on w for
four thermal gradients. 共c兲 Dependence on dT/dx for w⫽ 300
␮
m.
FIG. 3. 共a兲–共c兲 Mixing of two liquids 共black and white兲 by thermocapillary
convection induced by a transverse temperature gradient. The stripe is 500
␮
m wide, h
0
⫽ 20
␮
m, dT/dy⫽4 °C/mm, and
␮
⫽ 20 mPa s. The curves
shown in 共b兲 represent the streamlines of the convective flow. 共d兲 Experi-
mental positions
关
x(t),y(t)
兴
of 5-
␮
m-diam tracer particles in a rivulet flow-
ing at a 45° angle from the direction of ⵜT (w⫽ 530
␮
mand
␮
⫽ 18 mPa s). The time increment between subsequent data points is ⌬t
⫽ 6 s. The gray band signifies a portion of the slanted hydrophilic stripe.
658 Appl. Phys. Lett., Vol. 82, No. 4, 27 January 2003 Darhuber
et al.
Downloaded 15 Sep 2006 to 131.215.240.9. Redistribution subject to AIP license or copyright, see http://apl.aip.org/apl/copyright.jsp

discrete drops is shown in Fig. 4. The surface temperature is
electronically programmed through an array of embedded
heating resistors 共light gray兲. Discrete drops or continuous
streams can be moved along hydrophilic pathways 共orange兲
and directed around corners. Local temperature control al-
lows splitting of a liquid stream into droplets of predefined
volume. Figures 4共a兲–4共e兲 show the generation of a doublet
from a single drop. The rate of film thinning above a heated
resistor is essentially proportional to the heating power, but
independent of w and the film thickness.
21
The rupture of the
small connecting thread leaves behind satellite droplets,
which can be absorbed by dispatching one of the main drops
to collect the residue. The electrical power used to split and
propel drops of dodecane was typically less than 40 mW per
resistor. The power can be reduced by at least one order of
magnitude by using a polymeric substrate of low thermal
conductivity instead of glass.
22
Battery operation of this mi-
crofluidic device is, therefore, practicable.
Figures 4共f兲–4共l兲 depict electronic propulsion of discrete
droplets along partially wetting microstripes. The heating el-
ements are slightly narrower near the microstripe edges.
These constrictions increase the local resistive heating,
which causes a slightly elevated temperature at the stripe
edges. This helps center the streaming drops and films later-
ally. Figures 4共f兲–4共i兲 show a dodecane drop moving from
right to left through an intersection of two partially wetting,
1000-
␮
m-wide stripes on a glass substrate. Figures 4共j兲–4共l兲
show a drop being pulled around a corner. The average drop-
let speed
␯
d
is controlled by the electronic switching
interval—in Figs. 4共f兲–4共i兲
␯
d
⫽56
␮
m/s and in Figs. 4共j兲–
4共l兲,
v
d
⫽26
␮
m/s. In these series, the applied voltage was
2.36 V and the heater resistance 140 ⍀. The control algo-
rithm involved sequentially powering one resistor ahead of
the drop 共20 mW兲 and two resistors behind it 共⭐40 mW each
in a ramp-like fashion兲. The drop position is, therefore,
known to a precision equal to the resistor width, which is
advantageous for the simultaneous routing of a multitude of
droplets. On completely wetting surfaces, a thin residue film
can trail a moving droplet since the receding contact angle is
vanishingly small. Such residual films, which can cross con-
taminate liquid samples, can be eliminated, by making the
surface pathways partially wetting.
We have demonstrated that electronically addressable
heating arrays coupled with chemical surface patterning can
be used to actuate and manipulate continuous streams or dis-
crete drops of liquid on a solid substrate. Numerical simula-
tions for the flow speed of continuous microstreams are in
excellent agreement with experiment. Electronic control en-
ables transport with preset velocity, efficient mixing of sta-
tionary or moving liquids, and merging or splitting of liquids
into specified volumes. Temperature maps can be pro-
grammed to trap drops at a specified location for analysis
and synthesis. As the presence of an overlying liquid film
affects the thermal response time of the resistors, they can be
used as position sensors providing feedback control.
22
This
device can also serve as a chemical sensor since the liquid is
in continuous contact with the ambient vapor phase. The
variety of tasks that can be accomplished with high-
resolution thermal maps should, therefore, inspire alternative
designs for pocket-sized diagnostic devices.
This work is supported by NSF grant CTS-0088774,
MRSEC grant DMR-9809483, a NJCST grant, and an ND-
SEG fellowship 共J.M.D.兲.
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Si wafers were first coated with 200 nm SiN
x
and 200 nm SiO
2
, deposited
by plasma enhanced chemical vapor deposition 共PECVD兲 at 250 °C. A
100 nm Au layer was then deposited by an electron beam evaporation
共EBE兲 and patterned into heating elements using a lift-off technique. The
heating elements were passivated with 600 nm PECVD SiO
2
, on top of
which the chemical pattern was defined in a layer of perfluorooctyl-
trichlorosilane 共PFOTS兲 by photolithography. Ti heaters and Au contacts
were deposited on Corning 1737 glass slides by EBE. The hydrophilic
stripes were defined on a 200 nm PECVD SiO
2
layer using PFOTS.
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FIG. 4. 共a兲–共e兲 Thermally induced splitting of a dodecane drop on a par-
tially wetting stripe (w⫽ 1000
␮
m). The voltage applied to the microheater
共155 ⍀兲 was 2.5 V. The images were recorded at t⫽ 0, 6.0, 7.5, 8.0, and 8.5
s. 共f兲–共i兲 Dodecane drop propelled through an intersection outlined by the
dark gray pattern (w⫽ 1000
␮
m, time lapse 104 s兲. 共j兲–共l兲 Dodecane drop
turning a 90° corner 共time lapse 164 s兲.
659Appl. Phys. Lett., Vol. 82, No. 4, 27 January 2003 Darhuber
et al.
Downloaded 15 Sep 2006 to 131.215.240.9. Redistribution subject to AIP license or copyright, see http://apl.aip.org/apl/copyright.jsp

Frequently asked questions

Q1. What contributions have the authors mentioned in the paper "Microfluidic actuation by modulation of surface stresses" ?

The authors demonstrate the active manipulation of nanoliter liquid samples on the surface of a glass or silicon substrate by combining chemical surface patterning with electronically addressable microheater arrays. This method of fluidic actuation allows direct accessibility to liquid samples for handling and diagnostic purposes and provides an attractive platform for palm-sized and battery-powered analysis and synthesis.