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Electroactuation of Fluid Using Topographical Wetting Transitions Jean-Christophe Baret and Michel Decre´ Philips Research Laboratories Eindhoven, Prof. Holstlaan 4, 5656 AA Eindhoven, The Netherlands
Stephan Herminghaus and Ralf Seemann* Max Planck Institute for Dynamics and Self-Organization, D-37018 Go¨ ttingen, Germany Received August 16, 2005. In Final Form: October 6, 2005 The complex morphologies of liquids on topographically structured substrates are exploited for liquid actuation in open microchannels. The liquid is either confined in prefabricated grooves, thus forming elongated filaments, or gathers in macroscopic drops without invading the grooves, depending on conditions. Using the electrowetting effect, we can reversibly switch between these two states. The length of the filaments is sensitive to the ionic content of the liquid and can be described quantitatively with an electrical model considering the voltage drop along the groove.
Introduction The standard design of microfluidic systems, microchannels surrounded by a solid matrix,1,2 suffers from some serious drawbacks, the most obvious being its extreme sensitivity to clogging when the dimension of the channel is reduced on several microns and the expense of its fabrication. As a consequence, the development of novel concepts for microfluidics is a lively field in both technology and basic research. In particular, open concepts have been proposed as alternative microfluidic systems, in which the liquid is guided by wetting forces on a substrate which is artificially structured. An obvious advantage of this design is the direct accessibility, e.g., for cleaning. However, the inevitable presence of free liquid/vapor (or liquid/liquid) interfaces poses additional challenges. In particular, there are serious constraints on the free interface morphologies available. The liquid morphologies need to exhibit a constant mean curvature and positive second variation of their total surface to be dynamically stable. However, the interplay of the substrate structure with the free interface morphology via wetting forces may also be effectively exploited for actuation purposes. This aspect is addressed in the present study. There are in general two strategies for constructing open microfluidic systems. The first is to chemically pattern planar substrates and to prepare distinct surface domains which differ in their wettability.3-6 The second strategy is to use topographically structured surfaces, as can be fabricated by available standard photolithographic methods. It was recently shown that even relatively simple topographies such as steps7 and grooves with rectangular cross-sections8 exhibit a large variety of liquid morphol* To whom correspondence should be addressed. (1) See, for example: Thorsen, T.; Maerkl, S. J.; Quake, S. R. Science 2002, 298, 580. (2) Weigl, B. H.; Bardell, R. L.; Cabera, C. R. Adv. Drug Delivery Rev. 2003, 55, 349. (3) Gau, H.; Herminghaus, S.; Lenz, P.; Lipowsky, R. Science 1999, 283, 46. (4) Kataoka, D.; Troian, S. Nature 1999, 402, 794. (5) Wang, J.; et al. Nat. Mater. 2004, 3, 171. (6) Zhao, B.; et al. Science 2001, 291, 1023. (7) Brinkmann, M.; Blossey, R. Eur. Phys. J. E 2004, 14, 79.
ogies. In the case of grooves with rectangular cross section, this polymorphism is determined by only two parameters: the geometric aspect ratio X of the groove (i.e., its depth, a, divided by its width, b) and the contact angle θ of the liquid with the substrate material. Figure 1 displays the corresponding morphological diagram for rectangular grooves, cf. ref 8. The insets show optical micrographs of water droplets placed on grooved substrates with various wettability and aspect ratio. For small aspect ratios or a large contact angle, the liquid forms droplets with a lemon-like shape (i.e., slightly elongated, with pointed tips) that can extend over an arbitrary number of grooves (D). In this regime, it is energetically favorable for the liquid to collect as a droplet, rather than entering the grooves at any appreciable length. As the aspect ratio is increased, or the contact angle decreased, a transition occurs to a regime where this balance is reversed, and the liquid enters the grooves. It thus forms filaments, the Laplace pressure of which is found to be positive (F+). For an even larger aspect ratio, or even smaller contact angle, a second boundary line is crossed, beyond which the globally stable morphology consists of filaments with negative Laplace pressure (F-).8 Therefore, to obtain a certain liquid morphology, the surface topography and wettability must be matched by a careful choice of the two parameters X and θ. For microfluidic applications, the most interesting morphologies are extended liquid filaments for which the grooves act as confining microcompartments. Changing the wettability of the surface might lead to transitions between different wetting morphologies. Hence, by switching between a droplet morphology (D) and an elongated liquid filament (F), it is possible to transport liquid along prefabricated grooves. On the other hand, a local variation in the geometry of the groove only allows liquids with a certain contact angle to pass or require certain (over) pressure. Therefore, it seems feasible to realize microfluidic pumps and valves without moving parts. Fabricating grooves with local variation in the geometry only allows liquids with a certain wettability to (8) Seemann, R.; Brinkmann, M.; Kramer, E. J.; Lange, F. F.; Lipowsky, R. Proc. Natl. Acad. Sci. 2005, 102, 1848.
10.1021/la052228b CCC: $30.25 © 2005 American Chemical Society Published on Web 11/24/2005
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Figure 1. Morphological diagram as function of groove aspect ratio X and contact angle θ. The diagram contains three different regimes which involve liquid droplets (D) and filaments with positive (F+) and negative (F-) Laplace pressure. The insets show optical micrographs of the corresponding liquid morphologies. For the complete morphological diagram refer to ref 8. The data points show the experimental filling transitions derived from electrowetting experiments (see below).
pass or requires a certain (over) pressure, which might make valves without moving parts possible. Using special surface coatings that are sensitive to the droplet’s chemical content, temperature, or light9-12 may enable the fabrication of “smart microfluidic” systems that fill grooves with liquid or drain liquid off grooves, depending on external stimuli, like optoelectronic devices or bimetallic strips for electronic circuits. In the present study, we combine the grooved surface topography with electrowetting,13-17 which the contact angle θ to be varied continuously. Thus, liquid can be transported on demand along prefabricated grooves by switching between wetting morphologies. Experimental Section For electrowetting, an electrically conducting substrate is needed which bears a dielectric coating. When a conducting liquid is placed upon this substrate, a capacitor results. When a voltage is applied to it, the field energy stored in it leads to a decrease of the contact angle the liquid forms with the substrate. This can be a dramatic effect, spanning several tens of degrees.13-17 To exclude electrochemical effects, it is advantageous to use ac voltage, as was done in all experiments presented here. Using standard photolithographic methods combined with pulsed reactive ion gas etching, grooves have been fabricated in conductive arsenic-doped silicon wafers (see Figure 2a). Subsequently, an insulating oxide layer with thickness d of 1.15 ( 0.15 µm was thermally grown into the structured silicon sample. The resulting grooves have a width b ranging from 15 to 50 µm ( 1 µm and a fixed depth a of 20 ( 1 µm, yielding aspect ratios X ) a/b ranging from 0.40 to 1.33. To increase the initial contact angle of the liquid on the substrate the samples were hydrophobized depositing a self-assembled monolayer of OTS molecules (octadecyltrichlorosilane) on top, following standard procedures.18 The liquid we used was a mixture of 17 ( 3% water, 80 ( 3% glycerol, and 3 ( 2% salt by weight. The volume fractions were (9) Takei, Y. G.; Aoki, T.; Sanui, K.; Ogata, N.; Sakurai, Y.; Okano, T. Macromolecules 1994, 27, 6163. (10) Ichimura, K.; Oh, S.-K.; Nakagawa, M. Science 2000, 288, 1624. (11) Abbott, S.; Ralston, J.; Reynolds, G.; Hayes, R. Langmuir 1999, 15, 8923. (12) Lahann, J.; et al. Science 2003, 299, 371. (13) Quilliet, C.; Berge, B. Europhys. Lett. 2002, 60, 99. (14) Someya, T.; Dodabalapur, A.; Gelperin, A.; Katz, H. E.; Bao, Z. Langmuir 2002, 18, 5299. (15) Prins, M. W. J.; Welters, W. J. J.; Weekamp, J. W. Science 2001, 291, 277. (16) Mugele, F.; Baret, J.-C. J. Phys.: Condens. Matter 2005, 17, 705. (17) Lippmann, G. Ann. Chim. Phys. 1875, 5, 494. (18) Sagiv, J. J. Am. Chem. Soc. 1980, 102, 92.
Figure 2. (a) Scanning electron micrographs of rectangular grooves as used in the experiments. Right: the thermally grown oxide layer can be seen in a different gray level. (b) Top-view of a droplet imbibing into grooves for different (equidistant) voltages. The tips of the liquid filaments appear black in the optical reflection micrographs. (c) length of liquid filaments for different frequencies as function of the applied voltage. chosen such that the mixture is hygroscopically stable in our typical lab conditions. The corresponding conductivity of the mixture σ is 0.11 ( 0.04 S/m as measured by a HA8733 Hana conductometer. With our experimental system, the apparent contact angle θ for a drop of the liquid on the substrate can be tuned from about 95° without any voltage applied, down to about 45° for a voltage of 110 V. The apparent contact angle is independent of the frequency f of the applied voltage as well as of the position on the wafer, indicating a good lateral uniformity of the OTS-coating and the oxide layer.
Results and Discussion The series of optical micrographs in Figure 2b shows a typical filling transition experiment on grooves with an aspect ratio of X ) 1.33 at a frequency of f ) 20 kHz of the applied voltage. A feeding droplet acting as a reservoir is deposited on top of a grooved substrate, a platinum electrode is immersed into the droplet, and the voltage is slowly increased. The process is monitored in situ with an optical microscope and a digital camera. The tip of the liquid filament appears black in the reflection micrographs due to the slanted liquid interface near the contact line. The experiment shows a clear threshold behavior for the groove filling as predicted by the morphological diagram shown in Figure 1. Indeed, one expects the system to undergo a transition from a main droplet to filaments filling the grooves when the pressure inside the droplet exceeds that inside the
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filaments. For relatively large feeding droplets with a moderate curvature, one therefore expects the filling transition to occur close to the zero Laplace pressure curve separating the (F+) and (F-) regions in Figure 1. In Figure 2, one sees that, for applied voltages below the threshold voltage, the contact angle of the liquid on the substrate is lowered, but the liquid does not imbibe into the grooves. At the threshold, the liquid filaments start to leak into the grooves and grow if the voltage is further increased. Bringing the voltage back to zero after having reached the maximum voltage at the end of each experiment causes the liquid filaments to recede reversibly into the feeding drop. The length, l, of liquid filaments imbibing or draining off grooves essentially follows a modified Washburn equation, l2 ) γG(cos θ - cos θT)t/η, where γ is the surface tension of the liquid, η is its viscosity, and θT is the threshold contact angle for groove filling. G is the inverse flow resistance that is depending on the channel geometry. Additional filling experiments at different aspect ratios nicely confirm the location of the predicted filling transition close to zero Laplace pressure as shown in Figure 1 (red data points). A closer inspection reveals that the filling threshold is systematically shifted to larger contact angles than predicted by the morphological diagram. This is caused by the rather small size of the feeding droplet, the Laplace pressure of which is therefore slightly larger than zero (typically of order 100 Pa), thus shifting the transition line into the (F+) domain of Figure 1. Groove filling experiments using different drop sizes confirmed that the increasing Laplace pressure for smaller droplets shifts the filling transition to even larger contact angles. If the groove filling was solely governed by the relative capillary pressure between the feeding droplet and the filaments, one would expect the filaments to grow indefinitely inside the grooves when the filling threshold is exceeded. However, one readily sees from Figure 2 that the filaments extend to a finite length that increases with the applied voltage. To explore this behavior in more detail, we performed groove filling experiments keeping the volume of the drop and the aspect ratio of the grooves constant and varying the frequency f of the applied voltage as shown in Figure 2. We found a strong dependence of the length of the liquid filament not only on the applied voltage but also on its frequency. The threshold voltage for groove filling is independent of the frequency and shows that the filling transition is controlled by capillarity. Moreover the length of the liquid filament is determined solely by the electrical properties of the system and decreases strongly for increasing frequency. We attribute this to the fact that we use ac voltage in our experiments and that the conductivity of the liquid is finite, causing the voltage to drop along the liquid filament. Hence, the apparent Lippmann angle17 at the tip of the filament is larger than that at its inception from the drop. Indeed, we have noted that neither the apparent contact angle of the drop nor the filling threshold are affected by the frequency f of the applied voltage, from which we conclude that there is no significant voltage drop within the droplet, a consequence of its large electrical cross-section. One can therefore safely assume that the voltage at the foot of the groove is equal to the voltage applied to the feeding drop. Let us now proceed to quantify the voltage drop along the liquid filament in order to derive its length: we describe the liquid-filled groove as a conductive material surrounded by an insulating layer, which is electrically equivalent to a coaxial cable that can be described as a series of low passes along the direction of the groove.19 The equivalent coaxial cable of length l is free-ended.
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To calculate the resistance of the liquid filament δR and the capacitive impedance of the groove δC per unit of length, we assume the liquid filament to have a rectangular and constant cross-section (flat free-surface) all along the groove which leads to δR ) δz/(σba) and δC ) d/(jω0r(2a + b)δz), where z is the coordinate along the groove, ω ) 2πf, r ) 3.9 ( 0.2 is the dielectric constant of the insulating silicon oxide layer, 0 is the dielectric permittivity of vacuum, and j is the imaginary unit. The assumption of a constant cross section of the liquid filament is justified by the capillary model and the experimental verification that the filling occurs for about zero Laplace pressure. The differential equation governing the voltage profile along the liquid filament thus reads
u(z) δ2u ) 2j 2 2 δz λ
(1)
x
(2)
where
λ)
2dσ a ω0r 1 + 2X
is the natural length scale in this equation. It is composed of two characteristic length scales of our system: an electrical length scale 2dσ/(ω0r) representing the electrical properties of the material and a geometrical length scale, a/(1 + 2X). A direct consequence is that if we rescale the measured length of the filament shown in Figure 2c with ω1/2, we expect all data for different frequencies to collapse onto a single curve. That this is indeed the case is shown in Figure 3a. The dependence of the geometry of the groove, following eq 2, is also confirmed as shown in Figure 3b where rescaled filament length curves l(1 + 2X)1/2 for several aspect ratios also nicely superimpose. To account for the threshold voltage dependence on the aspect ratio X, we have also scaled the applied voltage u0 with the threshold voltage uT-1. Both data sets can be combined to a single master curve by scaling l with λ and u with uT-1 (not shown). An analytical expression for the voltage drop along a liquid filament of length l is obtained by solving eq 1 using as boundary conditions the facts that the voltage at the foot of the liquid filament is equal to the applied voltage u(z ) 0) ) u0 and that the current at the tip of the liquid filament is zero δu(z ) l)/δz ) 0. Moreover, the voltage right at the tip of the liquid filament corresponds to the filling threshold of the groove u(l) ) uT. Using the rescaled units z˜ ) z/λ, ˜l ) l/λ, u˜ (z˜ ) ) u(z˜ )/uT the solution reads
u˜ (z˜ ) ) xcosh2(l˜ - z˜ ) - sin2(l˜ - z˜ )
(3)
Replacing z˜ ) 0 and u˜ (0) ) u˜ 0 ) u0/uT in eq 3 provides an implicit relation between the applied voltage u˜ 0 and the length of the liquid filament ˜l. This curve cannot be inverted analytically and is numerically fitted to the experimental data (solid lines in Figure 3). The curve perfectly fits the experimental data using the experimentally determined geometry of the groove, the threshold voltage of 43 ( 2 V and the dielectric properties of the system as input parameters, and the conductivity of the liquid σ as sole fitting parameter. This yields a conductivity of σ ) 0.18 ( 0.02 S/m for the data set obtained from varying frequencies and σ ) 0.12 ( 0.02 S/m for those (19) Matrick, R. F. Transmission Lines for Digital and Communications Networks; McGraw-Hill: New York, 1969.
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sharp transition at threshold with a power law exponent of 1/4, as immediately seen by expanding eq 3 into a Taylor series, and second, the length of the liquid filament does not saturate with the applied voltage (eq 5). As a consequence, the maximum length of the liquid filament is only limited by the break-down voltage of the insulating layer. Hence, for technical applications, coatings with reduced defect densities or larger break through voltages will enable the filling of the longest grooves. In our experiments, we have easily achieved liquid filaments more than 100 times longer than the groove width for grooves with a ) 15 µm and X ) 1.33. Another important aspect of electrowetting on topographically structured substrates is the possibility to decrease the lateral dimension of the structures. From eq 2, we know that the length of the liquid filament scales with a1/2. The length of the filament in units of the groove depth l /a is thus proportional to a-1/2. Hence, according to our model, down scaling is not only possible but even increases the relative length of the liquid filament.
Figure 3. Master curve for the length of the liquid filament (a) as function of the applied voltage for different frequencies and (b) for different groove widths. The solid lines are obtained by numerically fitting eq 3 to the experimental data.
obtained from varying aspect ratios.20 This is in reasonable agreement with the experimental conductivity of σ ) 0.11 ( 0.04 S/m measured for typical lab conditions. This confirms the validity of our simple electrical model for the groove filling by electrowetting and bestows predictive value for open microfluidics on topographic substrates by electrowetting upon it. The asymptotic behavior of l as a function of the applied voltage is analytically obtained from eq 3
˜l ∼ (u˜ 0 - 1)1/4, u˜ 0 J 1
(4)
˜l ∼ ln(2u˜ 0), u˜ 0 f ∞
(5)
Each of these equations illustrates two salient properties of the groove filling: first, eq 4 describes an unusually
Conculsion In summary, we have demonstrated the sharply controlled filling of open grooves by electrowetting, from feeding droplets. Contrary to purely passive capillary filling controlled by the contact angle, alternate current electrowetting shows limited filling length of the filaments, which is described using a free-ended coaxial cable model. This allows the precise adjustment of the length of the liquid filaments by an external applied voltage. Furthermore, our electrical model predicts a dependence of the length of a filament on the conductivity of the liquid for a given voltage as l ∝ σ. Hence, the length should be sensitive to the chemical content of the liquid given that the ionic content and therefore the conductivity of the liquid varies with the chemical content. The asymptotic behavior of the filling length does not saturate with the applied voltage, as the filling is always supported by the threshold voltage at the tip of the filament. Electrowetting control of open topographic samples offers thus a simple and efficient actuation of open microfluidic chips. Generalizations of the geometries and the manipulation of the wettability explored here, toward a variety of “active components”, are straightforward. Acknowledgment. The authors thank Anton Kemmeren, Emil van Thiel, and Dirk Burdinski for help with sample preparation; fruitful discussions with Martin Brinkmann and Frieder Mugele are gratefully acknowledged. The project was supported by DFG priority program 1164 under grant number SE1118 and by Marie Curie Industry Host Fellowship IST-1999-80004. LA052228B (20) The two shown data sets were each measured on 1 day to neglect significant changes in the ambient lab conditions that might give rise to changes in the composition of the liquid mixture during the experiment.
