Principles of surface-directed liquid flow in microfluidic channels.

Article abstract of DOI:10.1021/ac020269w

To direct liquid flow inside microchannels, surface free energies were patterned by use of self-assembled monolayers (SAMs) in combination with either multistream laminar flow or photolithography. For the photolithographic method, two photocleavable SAMs

Full text of DOI:10.1021/ac020269w

Anal. Chem. 2002, 74, 4259-4268
Principles of Surface-Directed Liquid Flow in
Microfluidic Channels
Bin Zhao,† Jeffrey S. Moore,*,† and David J. Beebe‡
The Beckman Institute for Advanced Science and Technology, University of Illinois at UrbanasChampaign,
Urbana, Illinois 61801, and Department of Biomedical Engineering, The University of WisconsinsMadison,
Madison, Wisconsin 52706
mechanical pumping,3,4 electrowetting,5 electrochemistry,6 ther-
To direct liquid flow inside microchannels, surface free
energies were patterned by use of self-assembled mono-
layers (SAMs) in combination with either multistream
laminar flow or photolithography. For the photolitho-
graphic method, two photocleavable SAMs were designed
and synthesized. Carboxylic acid-terminated monolayers
were obtained by photodeprotection, which was confirmed
by contact angle and X-ray photoelectron spectroscopy.
Using either of these patterning methods, we show that
aqueous liquids flow only along the hydrophilic pathways
when the pressure is maintained below a critical value;
the liquids are referred to as being confined by virtual
walls. Several principles of liquid flow in surface-patterned
channels were derived analytically and verified experi-
mentally. These principles include the maximum pressure
that virtual walls can withstand, the critical width of the
hydrophilic pathway that can support spontaneous flow,
the smallest width of the liquid streams under an external
pressure, the critical radius of curvature of turns that can
be introduced into the hydrophilic pathway without liquid
crossing the hydrophilic-hydrophobic boundary, and the
minimal distance for two liquid streams to remain sepa-
rated under the maximum pressure. Experimental results
are in good agreement with the analytical predictions.
mocapillary pumping,7 and the use of magnetic fields.8
When the system is miniaturized to the submillimeter scale,
the surface-to-volume ratio increases dramatically. As a conse-
quence, surface properties of microchannels, especially wetting,
have significant effects on the liquid behavior, which is embodied
by the familiar phenomenon of liquids imbibing into glass
capillaries. The capillary rise has been the basis of a simple and
effective method to pump liquids into the microchannels.9 While
water spontaneously flows into a pristine glass capillary, it does
not penetrate a hydrophobically modified glass capillary unless
pressure is applied. We have taken advantage of these surface
effects to guide liquid flow inside surface-patterned microfluidic
channels.10
Handique and co-workers11,12 reported on the fabrication of
hydrophobic patches in microchannel networks to meter and
pump discrete liquid drops by thermopneumatic pressure. The
approach that they used is to modify the substrate surfaces with
hydrophobic self-assembled monolayers (SAMs) in selected areas
first and then align and bond substrates to form microchannel
networks. A desired method would simultaneously pattern surface
free energies on the top and bottom substrates in a preformed
microchannel. We choose to work with microchannels made from
glass slides and cover slips because their surface-wetting proper-
ties can be easily modified with SAMs and also because glass is
transparent, allowing the use of an optical microscope to study
liquid flow. It is well known that liquid flow is laminar in
microchannels, which means multiple liquid streams can flow side
In recent years, tremendous efforts have been invested in
miniaturizing and integrating chemical and physical processes
such as mixing, separation, purification, and detection to create
integrated microfluidic systems for chemical analysis and syn-
thesis and bioassay.1 The advantages of this so-called “lab-on-a-
chip” technology lie in the consumption of a small amount of the
sample and reagents, fast processing time, and high throughput
compared to macroscopic systems. A critical issue in the design
and fabrication of microfluidic devices is the manipulation of liquid
and gaseous fluids within microchannel networks. Many tech-
niques have been used to meter, transport, and position and mix
liquid samples. These techniques include electroosmotic flow,2
(3) Unger, M. A.; Chou, H. P.; Thorsen, T.; Scherer, A.; Quake, S. R. Science
2 0 0 0 , 288, 113-116.
(4) Fahrenberg, J.; Bier, W.; Maas, D.; Menz, W.; Ruprecht, R.; Schomburg,
W. K. J. Micromech. Microeng. 1 9 9 5 , 5, 169-171.
(5) Prins, M. W. J.; Welters, W. J. J.; Weekamp, J. W. Science 2 0 0 1 , 291, 277-
280.
(6) Gallardo, B. S.; Gupta, V. K.; Eagerton, F. D.; Jong, L. I.; Craig, V. S.; Shah,
R. R.; Abbott, N. L. Science 1 9 9 9 , 283, 57-60.
(7) Burns, M. A.; Mastrangelo, C. H.; Sammarco, T. S.; Man, F. P.; Webster, J.
R.; Johnson, B. N.; Foerster, B.; Jones, D.; Fields, Y.; Kaiser, A. R.; Burke,
D. T. Proc. Natl. Acad. Sci. U.S.A. 1 9 9 6 , 93, 5556-5561.
(8) Grant, K. M.; Hemmert, J. W.; White. H. S. J. Am. Chem. Soc. 2 0 0 2 , 124,
462-467.
* To whom the correspondence should be addressed. E-mail: moore@
scs.uiuc.edu.
(9) Delamarche, E.; Bernard, A.; Schmid, H.; Michel, B.; Biebuyck, H. Science
1 9 9 7 , 276, 779-781.
† University of Illinois at UrbanasChampaign.
‡ University of WisconsinsMadison.
(10) Zhao, B.; Moore, J. S.; Beebe, D. J. Science 2 0 0 1 , 291, 1023-1026.
(11) Handique, K.; Gogoi, B. P.; Burke, D. T.; Mastrangleo, C. H.; Burns, M. A.
Proc. SPIE-Int. Soc. Opt. Eng. 1 9 9 7 , 3224, 185-195.
(12) Handique, K.; Burke, D. T.; Mastrangelo, C. H.; Burns, M. A. Anal. Chem.
2 0 0 1 , 73, 1831-1838.
(1) Freemantle, M. Chem. Eng. News 1 9 9 9 , 77 (8), 27-36.
(2) Harrison, D. J.; Fluri, K.; Seiler, K.; Fan, Z. H.; Effenhauser, C. S.; Manz, A.
Science 1 9 9 3 , 261, 895-897.
10.1021/ac020269w CCC: $22.00 © 2002 American Chemical Society
Published on Web 06/28/2002
Analytical Chemistry, Vol. 74, No. 16, August 15, 2002 4259

Scheme 1. Photodeprotection of SAM of 2 upon UV Irradiation
by side without turbulence to maintain stationary interfaces.13 We
have taken advantage of this flow behavior to fabricate surface
patterns inside microchannels.10 Hexadecane and a solution of an
organotrichlorosilane (e.g., octadecyltrichlorosilane (OTS)) in
hexadecane were pumped into the preformed microchannels and
maintained under laminar flow for a predetermined period of time
until SAMs with full coverages formed. The areas where the silane
solution passed were modified with SAMs and became hydro-
phobic, while other areas remained hydrophilic. Once the surface
was patterned, aqueous solutions flow only along the hydrophilic
pathway, provided the pressure is maintained below a critical value
(thus we named the process surface-directed liquid flow). Because
there are no physical walls on the sides of the liquid streams, the
liquids are referred to as being confined by virtual walls. This
method is simple, and patterning is complete in a short time, but
it requires a preformed channel network and complex patterns
cannot be easily generated. To overcome the limitations of the
laminar flow fabrication method, we developed a photolithographic
method to pattern surface free energies inside microchannels.
With this method, all channel surfaces are first modified with
photocleavable SAMs and then patterned by use of photomasks
and UV light. The lithographic method is more flexible, allowing
complex surface patterns to be fabricated.
In this paper, we detail our studies on surface-directed liquid
flow from both theoretical and experimental approaches. The first
part of this article is the synthesis, characterization, and properties
of photocleavable SAMs. The second part consists of theoretical
analyses and experimental investigations of the principles underly-
ing the liquid flow inside surface-patterned channels. These
principles include the maximum pressure that virtual walls can
withstand, the critical width of the hydrophilic pathways that can
support spontaneous flow, the smallest width of the liquid streams
under an external pressure without entering the hydrophobic
regions, the critical radius of curvature of a turn that can be
introduced into the hydrophilic pathway without liquid crossing
the hydrophilic-hydrophobic boundary, and the minimal distance
for two liquid streams to remain separated under the maximum
pressure.
RESULTS AND DISCUSSION
Synthesis and Characterization of SAMs of Undecyl 4-(11-
Trichlorosilyl-1 -oxoundecyloxymethyl)-3 -nitrobenzoate (1 )
and 2 ,2 ,3 ,3 ,4 ,4 ,5 ,5 ,6 ,6 ,7 ,7 ,8 ,8 ,8 -P entadecafluoro-1 -octyl
4 -(1 1 -Trichlorosilyl-1 -oxoundecyloxymethyl)-3 -nitrobenzo-
ate (2 ). An essential requirement in designing a photocleavable
SAM for patterning surface free energies by ultraviolet (UV)
photolithography is that the functional groups must be cleaved
in long-wavelength UV light to avoid absorption by glass. o-
Nitrobenzyl and related groups have been widely used as photo-
cleavable protecting groups in organic synthesis and as photolabile
linkages in solid-state synthesis of peptides.14-16 These groups are
cleaved by UV light of wavelength longer than 320 nm, which is
suitable for our purpose. Two photocleavable SAMs were designed
by incorporation of o-nitrobenzyl groups, and their corresponding
organotrichlorosilanes 1 and 2 were synthesized. As illustrated
in Scheme 1, upon UV irradiation, the o-nitrobenzyl-oxygen bond
is cleaved, and thus carboxylic acid groups are exposed to the
air interface, making surfaces hydrophilic.
Synthesis of SAMs of 1 and 2 . Organotrichlorosilanes 1 and
2 were synthesized through a three-step route as illustrated in
Scheme 2. Esters 3 and 4 were prepared via a 1,3-dicyclohexyl-
carbodiimide (DCC) coupling reaction in yields of 65% and 64%,
respectively. The synthesis of 5 and 6 followed the procedure
reported by Shaw and co-workers.17,18 Hydrosilation of alkenes 5
and 6 in the presence of catalytic hydrogen hexachloroplatinate-
(14) Pillai, V. N. R. Synthesis 1 9 8 0 , 1-26.
(15) Amit, B.; Zehavi, U.; Patchornik, A. J. Org. Chem. 1 9 7 4 , 39, 192-196.
(16) Rich, D. H.; Gurwara, S. K. J. Am. Chem. Soc. 1 9 7 5 , 97, 1575-1579.
(17) Shaw, J. E.; Kunerth, D. C. J. Org. Chem. 1 9 7 4 , 39, 1968-1970.
(18) Shaw, J. E.; Kunerth, D. C.; Sherry, J. J. Tetrahedron Lett. 1 9 7 3 , 9, 689-
692.
(13) Kovacs, G. T. A. Micromachined Transducer Sourcebook; McGraw-Hill:
Boston, 1998.
4260 Analytical Chemistry, Vol. 74, No. 16, August 15, 2002

Scheme 2. Synthesis of Photocleavable H-SAM and F-SAM
(IV) hydrate afforded the desired products, which were confirmed
method described in previous publications.25,26 In the first ap-
1
by H and 13C NMR. However, the base peaks in mass spectra
proach, “piranha”-treated cover glasses were immersed into a
freshly prepared solution of 1 or 2 in dry hexadecane in a
scintillation vial at room temperature. The silane solution was also
injected into microchannels via a syringe. The optimal deposition
time varied from 30 min to 4 h, depending on the ambient
humidity, and was determined by measurement of advancing
contact angles of H2O on cover glasses. This approach is a
conventional method to deposit SAMs on a “piranha”-treated silica
substrate. In our experiments of formation of SAMs of 1 and 2
(in short, H-SAM and F-SAM, respectively), the deposition times
varied from sample to sample even though the apparent reaction
conditions were the same. Long deposition times lead to the
precipitation of polymer formed in the bulk solution. To avoid this
problem, a second method was used to prepare SAMs. A freshly
prepared solution of 2 in toluene was allowed to age for a period
until 1-min immersion of “piranha”-treated cover glasses resulted
in a H2O advancing contact angle of 118° for F-SAM.
obtained by field desorption are precursors (m/ z 517.3 compared
to m/ z 517.2 of 5 and m/ z 745.1 compared to m/ z 745.2 of 6 )
though the desired peaks m/ z 652.2 and 882.0 appeared in low
intensities. The trichlorosilyl groups were fragmented during
ionization. The final products were used for SAM deposition
without further purification.
High-quality SAMs of organotrichlorosilanes are not as easy
to obtain compared to SAMs of alkanethiolates.19-24 Although
extensive studies have been performed in the past two decades,
the mechanism of SAM formation remains controversial. Many
factors including organotrichlorosilane concentration, solvent,
water content in the solvent, surface hydration of the substrate,
humidity in the ambient environment, and temperature are known
to influence the quality and coverage of SAMs.20,21 Two approaches
were used to prepare photocleavable SAMs on cover glasses and
inside microchannels. Microchannels were made according to a
P hotodeprotection of H-SAM and F-SAM. Contact angle
and X-ray photoelectron spectroscopy (XPS) were used to study
the photodeprotection of H-SAM and F-SAM deposited on cover
glasses. Figure 1 shows the relationships between UV irradiation
time and the advancing contact angles (θa) of water and a NaOH
(19) Ulman, A. Introduction to Ultrathin Organic Films: From Langmuir-Blodgett
to Self-Assembly; Academic Press: San Diego, CA, 1991.
(20) Ulman, A. Chem. Rev. 1 9 9 6 , 96, 1533-1554.
(21) Liu, Y.; Wolf, L. K.; Messmer, M. C. Langmuir 2 0 0 1 , 17, 4329-4335.
(22) Bunker, B. C.; Carpick, R. W.; Assink, R. A.; Thomas, M. L.; Hankins, M.
G.; Voigt, J. A.; Sipola, D.; de Boer, M. P.; Gulley, G. L. Langmuir 2 0 0 0 ,
16, 7742-7751.
(23) Le Grange, J. D.; Markham, J. L.; Kurkjian, C. R. Langmuir 1 9 9 3 , 9, 1749-
1753.
(24) Tripp, C. P.; Hair, M. L. Langmuir 1 9 9 5 , 11, 149-155.
(25) Zhao, B.; Moore, J. S. Langmuir 2 0 0 1 17, 4758-4763.
(26) Beebe, D. J.; Moore, J. S.; Bauer, J. M.; Yu, Q.; Liu, R. H.; Devadoss, C.; Jo,
B.-H. Nature 2 0 0 0 404, 588-590.
Analytical Chemistry, Vol. 74, No. 16, August 15, 2002 4261

trend of θa decrease with irradiation time was observed but ∼60×
faster when Novacure (EFOS, model N2001-A1) with a 365-nm
filter was used as the UV light source with a preset intensity of
5600 mW/ cm2 and a distance between the lens and the channels
of 20 mm. The ability to control the surface wettability by UV
irradiation time gives us a means to continuously vary surface-
wetting properties. By combining this advantage and the principles
of surface-directed liquid flow, we have fabricated a series of
pressure-sensitive gates to regulate liquid flow.31
XP S Characterization. XPS is especially suitable for the study
of photodeprotection of H-SAM and F-SAM as o-nitrobenzyl groups
are cleaved after UV irradiation. In both spectra of H- and F-SAMs
before UV irradiation shown in Figures 2a and 3a, nitrogen peaks
N1s are found located at ∼405 eV, which are attributed to the
nitrogen in o-nitrobenzyl groups.32 Curves b in Figures 2 and 3
were recorded from a H-SAM and a F-SAM both irradiated by
UV light for 2.5 h. The nitrogen peaks at ∼405 eV were not
detectable. Although the fluorine peak shrank drastically after
irradiation in F-SAM, it did not disappear completely, which
implies that the photoreaction is not complete.
Figure 1. Effect of UV irradiation time on the surface-wetting
properties of H-SAM and F-SAM: (b) Advancing contact angles of
water on H-SAM; (9) advancing contact angles of water on F-SAM;
(2) advancing contact angles of pH ) 11.8 NaOH solution on H-SAM;
([) advancing contact angles of pH ) 11.8 NaOH solution on F-SAM.
Considering that the advancing contact angle of water changes
little with increasing UV irradiation time, some side reactions
might occur as discussed in the literature.14 A new nitrogen peak
was found at ∼400 eV, which we attributed to the contaminant
from air. It is known that the rate of contamination of acidic or
basic surfaces is rapid in air.33
solution (pH ) 11.8) on H-SAM and F-SAM. The θa of both H2O
and the NaOH solution decrease significantly during the early
irradiation period and level off after 90 min. The lowest values of
H2O θa on irradiated H-SAM and F-SAM are 58° and 66°,
respectively. The values of θa of the NaOH solution on both
irradiated H-SAM and F-SAM are ∼10° lower than those of water.
This is consistent with carboxylic acid-terminated surfaces as a
basic probe liquid ionizes the immobilized carboxylic acid groups
making the surface more wettable.27 The values of θa of both water
and the NaOH solution on F-SAM are ∼8° higher than those on
H-SAM after being irradiated by UV light for 3 h. XPS studies
indicate that the photochemical reaction is not complete or some
side reactions might occur (vide infra). A trace amount of fluorine
atoms on the surface can increase the observed advancing values
relative to alkyl chains, assuming the extent of photochemical
reactions is the same for both H-SAM and F-SAM. The values of
water θa on carboxylic acid-terminated monolayers achieved here
are much higher than those of water on carboxylic acid- or
hydroxyl-terminated SAMs of alkanethiolates (both are 0°)19 but
close to those of water on hydroxyl- and phenol-terminated
monolayers (63° and 58°, respectively) obtained via surface
reactions from the corresponding SAMs of trichlorosilanes.28,29
Besides the incomplete photodeprotection that will be discussed
later, there is another possible factor responsible for the high
values of water θa. The structures of SAMs of organotrichlorosi-
lanes are known to be less ordered than those from organothiols.
Polar functional groups on the surface are susceptible to surface
reorganization. More methylene groups exposed to the air
interface will make θa higher. The advancing contact angles of
water on hydroxyl-terminated monolayers have been reported to
be heavily dependent on how the samples are treated.19,30
Contact Angle Titration of Carboxylic Acid-Terminated
Monolayers. Contact angle titration is a method to study the
wettability of ionizable surfaces as a function of pH of the probe
liquids.33 We followed a procedure similar to those described in
the literature27,28,34 to perform contact angle titration of carboxylic
acid-terminated monolayers obtained by photodeprotection of H-
and F-SAMs. A series of aqueous buffered solutions prepared by
properly combining NaH2PO4, Na2HPO4, HCl solution, and NaOH
were used. The results are summarized in Figure 4. For both
surfaces, θa is independent of pH in the range of 2-5 and starts
to decrease at a pH of 5.5. Little change is observed at pH above
9.0. Clearly, the surface is more wettable at high pH values as
probe liquids of high pH values ionize carboxylic acid groups.
The changes of θa are reversible. Consider Young’s equation γlv-
cos θ ) γsv - γsl, where γlv, γsv, and γsl are surface free energies
of liquid-gas, solid-gas, and solid-liquid interfaces, respectively,
and θ is the contact angle. Assuming that γlv and γsv vary little
with respect to pH, the changes of γsl are responsible for the
decrease of contact angle at high pH values. If we assume that
the carboxylic acid groups are protonated at low pH (<5) and
completely ionized at high pH, we can infer the acidity of surface-
bound carboxylic acid pK1/ 2 as described by Lee and co-workers.33
pK1/ 2 is analogous to pKa in solution and is defined as the value
of the pH of the solution at which the functional groups at the
interface are half-ionized. Sigmoidal fitting indicates that the
transition (pK1/ 2) occurs at pH ) 6.90 and pH ) 7.05 for carboxylic
acid-terminated monolayers obtained from H- and F-SAMs,
Photodeprotection of H- and F-SAM can be much faster if a
higher intensity UV light source is used. For instance, a similar
(31) Zhao, B.; Moore, J. S.; Beebe, D. J. Manuscript to be submitted.
(32) Briggs, D. Surface Analysis of Polymers by XPS and Static SIMS; Cambridge
University Press: Cambridge, U.K., 1998.
(33) Lee, T. R.; Carey, R. I.; Biebuyck, H. A.; Whitesides, G. M. Langmuir 1 9 9 4 ,
10, 741-749.
(27) Bain, C. D.; Whitesides, G. M. Langmuir 1 9 8 9 , 5, 1370-1378.
(28) Zhao, B.; Mulkey, D.; Brittain, W. J.; Chen, Z.; Foster, M. D. Langmuir 1999,
15, 6856-6861.
(29) Heid, S.; Effenberger, F.; Bierbaum, K.; Grunze, M. Langmuir 1 9 9 6 , 12,
2118-2120.
(34) Holmes-Farley, S. R.; Reamey, R. H.; McCarthy, T. J.; Deutch, J.; Whitesides,
(30) Tillman, N.; Ulman, A.; Penner, T. L. Langmuir 1 9 8 9 , 5, 101-111.
G. M. Langmuir 1 9 8 5 , 1, 725-740.
4262 Analytical Chemistry, Vol. 74, No. 16, August 15, 2002

Figure 2. XPS spectra of H-SAM deposited on “piranha”-treated cover glasses (a) before and (b) after UV irradiation. (c) N1s area in curve a.
(d) N1s area in curve b.
respectively. Compared to the pKa of formic acid (3.74) and acetic
acid (4.76) in aqueous solutions, the values of pK1/ 2 derived here
are higher by about 2-3 pH units. These results are consistent
with that of carboxylic acid on a polyethylene surface obtained
by chromic acid oxidation.34 Holmes-Farley and co-workers
attributed the shift of pK1/ 2 relative to the solution pKa to the
difficulties in the formation of carboxylate ions at the solid-liquid
interface due to the low dielectric constant at the interface or
charge-charge interaction.34
The contact angle titration studies thus provide further
evidence that carboxylic acid-terminated monoloayers were ob-
tained by photodeprotection of H- and F-SAMs. We have taken
advantage of the changes of advancing contact angles with respect
to pH to fabricate pH-sensitive gates to regulate liquid flow inside
surface-patterned channels.31
P rinciples of Surface-Directed Liquid Flow inside Micro-
channels. In this section, we discuss the principles underlying
the liquid flow in surface-patterned microfluidic channels using
both analytical and experimental approaches. A variety of hydro-
philic-hydrophobic surface patterns have been fabricated by use
of either the laminar flow or photolithography fabrication method.
P rinciple 1 : Critical P ressure That Virtual Walls Can
Withstand. Aqueous solutions flow only along the hydrophilic
pathways in surface-patterned microchannels when the pressure
is maintained below a critical value. The gas-liquid interface is
pinned precisely at the boundary between the hydrophilic and
hydrophobic regions, and the liquid will curve outward if a
pressure is applied (Figure 5). Liquid streams will rupture the
virtual walls and flow into the hydrophobic regions if the angle of
curvature of the liquid at the hydrophilic-hydrophobic boundary
(θb) equals the advancing contact angle of the liquid on the
nonpolar surface (θn). When a liquid surface is curved, there is a
pressure drop across the interface due to the liquid surface
tension. This is described by the Young-Laplace equation, ∆P )
γ(1/ R1 + 1/ R2), where ∆P is the pressure difference, γ is the
liquid surface tension, and R1 and R2 are the radii of curvature in
directions vertical and parallel to the liquid stream.35 For a straight
stream, the equation is simplified to ∆P ) γ/ R1. The parameter
R1 is related to the channel depth h and θb through the equation,
R1 ) h/ [2 sin(θb - 90°)]. When θb ) θn, the maximum pressure
that virtual walls can sustain in a straight stream, is realized, Pmax
) ∆P ) (2γ/ h) sin(θn - 90°). Obviously, θn must be greater than
90° for liquids to be confined to the hydrophilic regions by virtual
walls. Experimentally, we observed that hexadecane was not
confined to the hydrophilic pathways generated from photocleav-
able F-SAM, which is consistent with the fact that the θn of HD
on F-SAM is 74°, i.e., smaller than 90°.36 The channel depth is
∼180 µm, and the values of θn of water on SAMs of OTS and
heptadecafluoro-1,1,2,2-tetrahydrodecyltrichlorosilane (HFTS) are
112° and 118°, respectively. Calculations show that the Pmax for
OTS and HFTS are 300 (30.6 mm H2O) and 376 N/ m2 (38.4 mm
H2O), respectively. We used surface-patterned channels fabricated
by multistream laminar flow in combination with SAMs of either
OTS or HFTS to measure the maximum pressures. Experimental
results are 31-mm water for OTS-patterned channels and 37-mm
water for HFTS-patterned channels, in good agreement with our
analytical predictions.10
P rinciple 2 : Critical Width of the Hydrophilic P athways
That Can Support Spontaneous Liquid Flows. Figure 6a
illustrates the tip of an advancing liquid stream in a surface-
patterned channel. The advancing contact angle of water on virtual
walls can be viewed as 180° since small water drops assume a
(35) Adamson, A. W. Physcial Chemistry of Surfaces, 5th ed.; Wiley: New York,
1990.
(36) Zhao, B. Viernes, N. O. L.; Moore, J. S.; Beebe, D. J. J. Am. Chem. Soc.
2 0 0 2 , 124, 5284-5285.
Analytical Chemistry, Vol. 74, No. 16, August 15, 2002 4263

Figure 3. XPS spectra of F-SAM deposited on “piranha”-treated cover glasses (a) before and (b) after UV irradiation. (c) N1s area in curve a.
(d) N1s area in curve b.
Figure 5. Angle of curvature θb of a liquid confined to the hydrophilic
region inside a microchannel.
does not spontaneously flow through the hydrophilic region. The
critical condition occurs when |R2| is equal to |R1| (i.e., ∆P ) γ-
(1/ R1 + 1/ R2) ) 0), which is satisfied when w ) h/ (cos θp). If
the hydrophilic region is completely wetted by aqueous liquids
Figure 4. Advancing contact angles of aqueous buffered solutions
(θp ) 0°), the critical width of the liquid stream is equal to the
channel depth. A higher contact angle in the hydrophilic pathway
requires a larger width for flow to take place spontaneously.
We used a wedge-shaped photomask shown in the upper left
corner of Figure 6d to fabricate a surface pattern inside a channel
to verify the above analytical expression. The channel surface was
deposited with F-SAM. The UV irradiation time was 2 h. The
introductory pathway was also irradiated so that liquids flow
spontaneously through the entrance. Figure 6d and e shows the
optical micrographs of where water and the NaOH solution (pH
) 11.8) reached in the wedge-shaped hydrophilic pattern under
spontaneous flow conditions. The images were taken when liquids
did not move forward any more (it took a few minutes after liquids
were introduced). The tips of both liquid streams exhibit round
shapes as expected in the theoretical analysis. We used circles to
fit the tips, and the diameters of the fitting circles are 442 and
359 µm for water and the NaOH solution, respectively. By use of
on carboxylic acid-terminated monolayers obtained from H-SAM and
F-SAM by UV irradiation. (b) Monolayer obtained from H-SAM; (9)
monolayer obtained from F-SAM. The curves were from sigmoidal
fitting.
round shape in air. The aqueous solution in the hydrophilic
pathway is actually confined by top and bottom hydrophilic
surfaces separated by distance h and two hydrophobic virtual walls
spaced by width w. The capillary force generated from the
hydrophilic surfaces drives liquid forward as in a pristine glass
capillary, producing a side-view profile shown in Figure 6b with a
negative R1, whereas the retraction force generated from the
hydrophobic virtual walls drags water backward, producing a top-
view profile shown in Figure 6c with a positive R2. These two
forces counteract each other and determine the critical geometry
of the pathway. If |R2| > |R1|, ∆P < 0 and water spontaneously
wets the hydrophilic pathway. If |R2| < |R1|, ∆P > 0 and water
4264 Analytical Chemistry, Vol. 74, No. 16, August 15, 2002

Figure 6. (a) Schematic illustration of the tip of a liquid advancing along a hydrophilic pathway. (b) Side-view profile and (c) top-view profile
of the tip of the advancing liquid stream confined to the hydrophilic pathway. Optical micrographs of where water (d) and the pH ) 11.8 NaOH
solution (e) stop in a wedge-shaped pathway under spontaneous flow conditions. The dash circles are used to fit the tips of liquid streams for
determination of the critical widths. The surface pattern was fabricated by use of the photomask shown in the upper left corner of image d.
the critical width equation derived above, the calculated advancing
contact angles of water and the NaOH solution on the hydrophilic
region are 66° and 60°, which are in good agreement with the
results measured on a F-SAM-coated cover glass irradiated by
UV light for the same length of time (69° and 59° for water and
the NaOH solution (pH ) 11.8) in Figure 2, respectively).
P rinciple 3 : Smallest Width of Liquid Streams under
External P ressures. If a pressure is applied to a liquid stream
confined to the wedge-shaped hydrophilic region, it will flow into
a narrower portion of the hydrophilic pathway. As discussed in
principle 2, the pressure drop across the liquid interface in the
tip of a liquid stream is described by Young-Laplace equation
∆P ) γ (1/ R1 + 1/ R2), where R1 and R2 are defined as the radii
of curvature in directions vertical and parallel to liquid stream.
The critical condition under an external pressure occurs when
the sum of the external pressure and capillary force γ/ R1
generated from the hydrophilic physical walls equals the retraction
force generated from hydrophobic virtual wall γ/ R2; that is, P +
γ/ R1 ) γ/ R2. The pressure, P, can be expressed in terms of the
water height H. Therefore, 1/ w ) (Fg/ 2γ)H + cos θp/ h ) (Fg/
2γ)H + 1/ wo, where F is the liquid density and wo is the critical
width of liquid streams under spontaneous flow conditions.
Experimentally, we used a wedge-shaped hydrophilic surface
pattern to investigate the smallest width of liquid streams under
external pressures. The images were taken when the liquid was
no longer moving under a certain pressure. The tip was fitted
with a circle, and the diameter was measured. Figure 7 shows
the calculated values and experimental results of the smallest
width of a liquid stream under external pressures. Although the
trend of the decrease in the smallest width with increasing
external pressure is qualitatively consistent with the theoretical
curve, there is a discrepancy between the theoretical predictions
and experimental data. This discrepancy may come from some
factors that have not been taken into account. For example, the
advancing contact angle of an aqueous liquid on the hydrophilic
region surrounded by the hydrophobic surface under a pressure
may not be the same as obtained in the contact angle measure-
ment. More investigations regarding this issue are needed and
are underway.
P rinciple 4 : Critical Radius of Curvature of Turns That
Liquids Can Make under Spontaneous Flow Conditions.
Liquids do not have their own shapes but assume the shapes of
their containers. In surface-patterned channels, water is confined
to the hydrophilic region by only two physical walls, raising
questions such as how well the liquid shape can be controlled. If
a turn is introduced in the hydrophilic pathway as illustrated in
Figure 8a, the radius of curvature in the direction parallel to the
liquid stream, R2, is finite. For the outer virtual wall, R2 is positive
and thus the maximum pressure that the outer virtual wall can
withstand increases. For the inner virtual wall, R2 is negative, and
consequently, the maximum pressure decreases. Thus, there is
a limit on the sharpness of the turns that can be introduced
without the liquid crossing the boundary. The critical condition
occurs at ∆P ) 0, that is, R1 ) R2i. The smallest R1 is realized
Analytical Chemistry, Vol. 74, No. 16, August 15, 2002 4265

Figure 7. Relationship between the smallest width of liquid stream and external pressures. (b) Experimental results; ([) calculated values.
Optical micrographs of where water stops at a pressure of (a) 0 and (b) 17.5 mm H2O in a wedge-shaped hydrophilic surface pattern. The dash
circles are used to fit the tips of liquid streams for determination of the critical widths.
Figure 8. (a) Top-view profile of a turn introduced into a hydrophilic pathway. (b) Side-view profile along the dash line in the top-view profile.
Optical micrographs of (c) water and (d) pH ) 11.8 NaOH solution streams making turns. The dash circles are used to fit the inner edges for
determination of the critical radius of curvature of turns. The surface pattern was fabricated by use of the photomask shown in the upper left
corner of image c in a reduced scale. The images were taken when liquid edges were no longer moving.
when θb ) θn. Therefore the critical radius of curvature is |R2ic
|
We used a photomask shown in Figure 8c to fabricate a surface
pattern inside a F-SAM-coated channel. The introductory pathway
was also irradiated by UV light so that aqueous solutions can
advance into the hydrophilic pathway spontaneously. Figure 8c
and d shows the images of water and the NaOH solution (pH )
) |R1| ) h/ [2 sin(θn - 90°)]. For h ) 180 µm as used here,
calculation shows that the critical radii of curvature of the turns
are 240 µm in H-SAM-modified channel and 192 µm in F-SAM-
modified channels.
4266 Analytical Chemistry, Vol. 74, No. 16, August 15, 2002

Figure 9. (a) Top-view profile of two liquid streams separated by a hydrophobic stripe with a width of dm. (b) Side-view profile of two liquid
streams remaining separated under the maximum pressure. (c) The photomask used in the fabrication of two hydrophilic pathways separated
by a 50-µm hydrophobic stripe. Optical micrographs of water streams (d) under spontaneous flow conditions, pressures of (e) 5- and (f) 12-mm
water.
11.8) flowing into the hydrophilic pathways spontaneously. The
images were recorded when the edges were no longer moving
(∼10 min after the solution was introduced). As expected, the
inner edges smoothed out and exhibited rounded shapes. More-
over, they are thicker than the straight edges, which indirectly
indicates the liquid-gas interface curves outward. We used circles
to fit the inner edges and measured the diameters of the circles.
The results were 391 and 432 µm for water and the basic solution
streams, respectively, close to the calculated values (384 µm). The
advancing contact angles of water and the basic solution were
the same on the F-SAM surface. The differences between the radii
of curvature of turns made by water and the NaOH solution are
attributed to kinetic factors. It was observed that the flow rate of
the basic solution was higher than water on the same hydrophilic
pathways due to its lower advancing contact angle. This kinetic
factor causes the NaOH solution to flow into the hydrophobic
region more than under an equilibrium condition. Obviously,
liquids cannot make a very sharp turn because of the liquid surface
tension effect. However, if we decrease the channel height and
increase the advancing contact angle (e.g., through controlling
the surface roughness37), it would be possible to better control
the liquid shape.
is desired for fabricating compact microfluidic devices and for
performing fast manipulations. In surface-directed liquid flow,
two liquid streams can be extremely close to each other while
remaining separated under a condition of no pressure if the
boundary between the hydrophilic and hydrophobic regions is
ideally sharp. An external pressure applied to the liquid streams
will cause the gas-liquid interface to bulge out and flow into the
hydrophobic region if the angle of curvature θb at the hydrophilic-
hydrophobic boundary equals the θn of the liquid on the
hydrophobic region. Figure 9a and b shows the top-view and side-
view profiles of two liquid streams flowing parallel to each other
separated by a hydrophobic stripe of width d under the maximum
pressure. The minimum distance for two streams to remain
separated under the maximum pressure can be calculated on the
assumptions that the boundary between the hydrophilic and
hydrophobic regions are infinitely sharp and two gas-liquid
interfaces come in contact at the critical condition θb ) θn as
shown in Figure 9b. Thus, the minimum distance is dm ) 2[R1 -
R1 cos(θn - 90°)] ) h[1 - cos(θn - 90°)]/ sin(θn - 90°). It is
apparent that the minimum distance is determined by two
parameters, h and θn. Calculations indicate that the values of dm
for water in patterned H-SAM- and F-SAM-coated channels are
35 and 45 µm, respectively for h of ∼180 µm.
P rinciple 5 . Minimum Distance for Two Liquid Streams
To Remain Separated under the Maximum P ressure. A high
density of microchannels or liquid streams in a microfluidic chip
We patterned a surface consisting of two hydrophilic stripes
separated by a 50-µm hydrophobic stripe by use of the photomask
shown in Figure 9c inside a F-SAM-coated channel. The UV
(37) Johnson, R. E.; Dettre, R. H. Adv. Chem. Ser. 1 9 6 4 , 43, 112.
Analytical Chemistry, Vol. 74, No. 16, August 15, 2002 4267

irradiation time was 130 min. Water flowed into the hydrophilic
regions spontaneously (Figure 9d). Figure 9e and f shows the
images of water streams under pressures of 5- and 12-mm water,
respectively. Although we could not image the side-view profile,
it is clear that the boundaries of the liquid streams became thicker
and approached one another with increasing the pressure, which
indirectly indicated that the gas-liquid interface bulged out.
Owing to the intrinsic resolution limit of transparency film
photomasks, the boundary between the hydrophilic and hydro-
phobic regions is more or less distorted on the scale of ∼10 µm.38
Since the channel depth is ∼180 µm, more than 3 times larger
than the hydrophobic gap, the fidelity between the photomask
and surface patterns on top and bottom substrates is also
dependent on whether the UV light is perfectly columnated. We
speculate that these two factors are responsible for the defect
appearing in images c and d. Nevertheless, we have shown that
the resolution of surface patterns fabricated by use of our current
photolithography method can reach ∼20 µm.
pressure that virtual walls can withstand in a straight stream is
Pmax ) (2γ/ h) sin(θn - 90°). The critical width of the hydrophilic
pathways that can support spontaneous liquid flow is w ) h/ (cos
θp). The smallest width that allows liquid stream to flow in under
an external pressure is 1/ w ) (Fg/ 2γ)H + cosθp/ h. The critical
radius of curvature of turns that can be introduced in the
hydrophilic pathways without liquid flowing into the hydrophobic
regions is h/ [2 sin(θn - 90°)]. The minimum distance for two
liquid streams to remain separated under maximum pressure is
dm ) h[1 - cos(θn - 90°)]/ sin(θn - 90°). A series of surface
patterns were designed and fabricated inside channels to verify
these equations. Experimental results are in good qualitative
agreement and generally good quantitative agreement with the
analytical values. Because surface-directed liquid flow requires
only two physical walls, a large gas-liquid interface is created,
which enables gas-liquid reactions to be performed in a more
controlled way.10 We believe that the principles underlying surface-
directed liquid flow and the methods that we developed to
generate surface patterns will find a broad range of applications
in microfluidic systems including chemical and biological analysis
and microreactors, especially where gaseous fluids are involved.
Conclusions. SAMs were used in combination with either
multistream laminar flow or photolithography to pattern surface
free energies inside channels to direct liquid flow. Aqueous
solutions flow only along the hydrophilic pathways provided the
pressure is maintained below a critical value. For use in photoli-
thography, two photocleavable SAMs of organotrichlorosilanes
were designed and successfully prepared. Photodeprotections
were investigated by contact angle, XPS, and contact angle
titration. XPS study indicated that the photodeprotection reaction
was close to complete after UV irradiation for 2.5 h. A small
fluorine peak existing in the XPS of the UV-irradiated F-SAM and
little change in contact angle with a longer irradiation time implied
that some side reactions occur. Contact angle titration further
proved that carboxylic acid-terminated monolayers were obtained.
The acidities, pK1/ 2, of surface-bound carboxylic acid obtained from
H- and F-SAM were derived from the titration curves and were
found to be 2-3 pH units higher than the solution pKa. Although
these two SAMs perform similarly, their differences in initial values
of θa and final values of θa after UV irradiation give us a flexibility
in controlling surface wettabilities. The principles governing the
liquid flow in the surface-patterned channels were investigated
analytically and experimentally. The analytical equations were
derived based on the Young-Laplace equation. The maximum
ACKNOWLEDGMENT
This work was financially supported by grants from the
Defense Advanced Research Projects Agency-MTO F30602-00-1-
0570 and NSF DMR 01-06608. XPS measurements were carried
out at the Materials Research Laboratory center for Microanalysis
of Materials, which is supported by the Department of Energy
through Grant DE FG0296R45439. Funding for the Kratos Axis
ULTRA XPS system was provided by the National Science
Foundation through Grant NSFDMR 99-77482 and the State of
Illinois. We acknowledge Dr. Rick Haasch for his help in XPS
measurement.
SUPPORTING INFORMATION AVAILABLE
Experimental procedure for the preparation of 1 and 2 and
their characterization data. Experimental procedure for H-SAM
and F-SAM formation and photodeprotection. This material is
available free of charge via the Internet at http:/ / pubs.acs.org.
Received for review April 25, 2002. Accepted May 22,
2002.
(38) Love, J. C.; Wolfe, D. B.; Jacobs, H. O.; Whitesides, G. M. Langmuir 2 0 0 1 ,
17, 6005-6012.
AC020269W
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