Directed Drop Transport Rectified from Orthogonal Vibrations via a

Article pubs.acs.org/Langmuir

Directed Drop Transport Rectified from Orthogonal Vibrations via a Flat Wetting Barrier Ratchet Todd A. Duncombe,†,‡ James F. Parsons,§ and Karl F. Böhringer*,‡,∥ ‡

Department of Electrical Engineering, §Department of Computer Science and Engineering, and ∥Department of Bioengineering, University of Washington, Seattle, Washington 98195, United States S Supporting Information *

ABSTRACT: We introduce the wetting barrier ratchet, a digital microfluidic technology for directed drop transport in an open air environment. Cyclic drop footprint oscillations initiated by orthogonal vibrations as low as 37 μm in amplitude at 82 Hz are rectified into fast (mm/s) and controlled transport along a fabricated ratchet design. The ratchet is made from a simple wettability pattern atop a microscopically flat surface consisting of periodic semi-circular hydrophilic features on a hydrophobic background. The microfluidic ratchet capitalizes on the asymmetric contact angle hysteresis induced by the curved features to drive transport. In comparison to the previously reported texture ratchets, wetting barrier ratchets require 3-fold lower actuation amplitudes for a 10 μL drop, have a simplified fabrication, and can be made optically flat for applications where transparency is paramount.

1. INTRODUCTION Digital microfluidics (DMF) is a lab-on-a-chip platform for the processing of discrete liquid volumes that prevents crosscontamination between samples and dilution by diffusion. The majority of DMF technologies transport drops by establishing thermodynamic gradients. This can be achieved passively through a predetermined, static energy gradient1−3 or actively through local, dynamic gradients controlled by a stimulus, such as thermocapillary wetting4 or electrowetting on dielectric.5 An emerging alternative to gradient transport is ratcheting. DMF ratchets have characteristics incorporating both passive and active transport schemes. Ratchets use a predetermined asymmetry (either in fabrication6 or actuation7) to rectify an energy input into controlled transport.8,9 This offers drop control over long distances through a potentially simple, low power actuation mechanism.10 Recently, we reported the texture ratchet,10 a hydrophobic rough diplanar surface made of silicon or elastomer. The “pawl” of the texture ratchet is a microfabricated track consisting of periodic curved semi-circular rungs. When a drop is placed on the track, it contacts only the upper plane of the rough diplanar surface in its Cassie−Baxter (CB) state. As a result of the semicircular rung design, there is near-continuous pinning for the side of the drop aligned with the rung curvature but only intermittent pinning for the anti-aligned side. The asymmetry in pinning results in unbalanced contact angle hysteresis. When sufficiently agitated by vertical vibration, the contact line of the drop will depin to cyclically advance and recede. Asymmetry in contact angle hysteresis rectifies footprint oscillations into controlled horizontal transport, specifically, in the direction of the rung curvature, or greater contact angle hysteresis. The use of perpendicular vibrations makes the DMF platform more © 2012 American Chemical Society

versatile than parallel vibration ratchets, because multiple drops can be directed in arbitrary directions (including along circular paths10) with a single unvarying actuation source. Texture ratchets capitalize on strong pinning at geometric barriers, but they are inherently limited by the nature of rough surfaces. At extreme vibrations, the drop can collapse from the CB state into the microstructure and become immobilized in the Wenzel state.11 In addition, aspect-ratio fabrication constraints limit the minimal ratchet period length achievable on a microstructured surface. Fully transparent texture ratchets are impossible to realize. The fabrication protocols required for a rough surface limit the concurrent fabrication and integration of electrodes and sensors. To realize a ratchet on a flat surface, we chemically patterned hydrophilic regions (contact angle θ1) on a hydrophobic background (contact angle θ2), with θ1 < θ2. In contrast to geometric discontinuities in texture ratchets, the wetting barrier ratchet uses a periodic, semi-circular, chemically heterogeneous pattern to induce asymmetric contact angle hysteresis. We report two surface modification techniques using both oxide and gold-adhering self-assembled monolayers (SAMs) to pattern the wettability of a surface. Trimethylsilanol (TMS)− dodecanethiol and TMS−perfluorooctyltrichlorosilane (FOTS) ratchets are displayed in panels A and B of Figure 1, respectively. In this paper, we compare the performance between texture ratchets and wetting barrier ratchets and investigate the role of rung curvature in establishing asymmetry and ratcheting performance. Received: June 14, 2012 Revised: August 28, 2012 Published: August 30, 2012 13765

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Figure 1. Wetting barrier ratchets transport drops using periodic semi-circular hydrophilic rungs on a hydrophobic background. (A) TMS− dodecanethiol wetting barrier ratchet. Dark regions correspond to the hydrophilic TMS rungs, and lighter areas correspond to the hydrophobic dodecanethiol self-assembled on Au. (B) A sessile drop sits on an optically flat TMS−FOTS wetting barrier ratchet. (C) For visualization purposes, we overlay photos from the edges of a receding drop with the CAD mask design of the wettability pattern. The right (leading) edge of the drop conforms to rung curvature, while the left (trailing) edge crosses several rungs. The resulting asymmetric pinning is estimated by examining the portion of the TPL, which lies at the hydrophilic−hydrophobic boundary (indicated in red). For the leading edge, 100% of the TPL resides at the boundary between the hydrophilic−hydrophobic regions, while for the trailing edge, only 29% does.

where θapp, θ1 and θ2, and θb are the apparent contact angle, the equilibrium contact angles for the hydrophilic and hydrophobic materials, and the contact angle at the boundary, respectively. The line fraction χi is the proportion of the TPL length on the given materials or along the boundary projected orthogonally to the direction of pinning, such that χ1 + χ2 + χb = 1. To solve for cos θR and cos θA from eq 2, we assume that recession occurs when θb = θ1 and advancement occurs when θb = θ2.17,28 The results are substituted into eq 1 to derive the direct relationship between the force of pinning to the boundary line fraction χb and the difference in the contact angle cosines of the two surfaces.

2. THEORY When a drop is placed on a flat chemically homogeneous surface, the contact angle at the three-phase boundary can be characterized by the Young−Dupré equation.12 However, this equation does not hold if the triple line (TPL) coincides with a wetting discontinuity, where a range of contact angles can be established. Pinning is observed as contact angle hysteresis, i.e., as the difference between the apparent advancing (θA) and receding (θR) contact angles. The metastable state of a liquid on geometric discontinuities was first considered by Gibbs13 and later experimentally confirmed by Oliver et al.14 More recently, a similar effect was described at chemical discontinuities15−17 between regions of varying wettability. For our purposes, it is useful to define a hysteresis force (FHys) as the difference between the pinning force at the TPL18 for the advancing and receding state FHys = wγ(cos θR − cos θA)

FHys = χb wγ(cos θ1 − cos θ2)

On a ratchet using periodic curved rungs as its pawl, an asymmetric boundary line fraction is established between the portion of the drop edge aligned with the curvature and the portion of the drop edge that is anti-aligned with the curvature of the rungs (Figure 1C). We denote the former as the leading edge (high χb) and the latter as the trailing edge (low χb) of the drop. The effectiveness of the ratchet in converting orthogonal perturbations to anisotropic drop motion is related to relative hysteresis of the leading and trailing edges (eq 4). This can be found by considering the difference in hysteresis force between the leading and trailing edges of a drop.

(1)

where w is the width of the drop projected orthogonally to the direction of pinning and γ is the solid−liquid surface tension. Using this projection, we effectively extract the component of the force vector FHys in one direction of pinning.18 For a drop placed on a heterogeneous surface, the classic CB equation19 predicts the apparent contact angle by an area-weighted average of the cosines of the material contact angles. Recently, several papers17,20−26 have pointed out the limitations of the CB equation for surfaces with non-uniform pinning27 at the TPL and proposed modified CB equations.20,24,25 In this paper, we use the line-fraction-modified CB equation,20,21,23 which enables a simple and intuitive means for describing our system. When a drop is placed on the device, fractions of the TPL lie on the hydrophilic region, the hydrophobic region, and the boundary between the two wettabilities. The portion of the TPL at the boundary accounts for the majority of hysteresis, because its local contact angle (θb) can vary between the equilibrium contact angles of the two materials before it depins (θ1 < θb < θ2). Using the line fraction method, we can relate the apparent contact angle to the alignment of the TPL on a heterogeneous surface cos θapp = χ1 cos θ1 + χ2 cos θ2 + χb cos θ b

(3)

FAnisotropy = (χb,Lead − χb,Trail )wγ(cos θ1 − cos θ2)

(4)

This equation provides a useful design principle for optimizing performance. Surfaces that maximize the boundary line fraction along the leading edge while minimizing the boundary line fraction along the trailing edge will produce the greatest anisotropy and ratcheting performance. The boundary line fractions χb,Lead and χb,Trail are determined by the complex interaction between a drop and a ratchet design; rung period, rung width, track width, rung curvature, and surface hydrophobicity, in addition to drop volume, surface tension, and position on the track, all play a critical role. Until more accurate models are developed for predicting boundary line fractions and measuring them, eq 4 is useful for qualitative design comparisons but not (yet) for precise calculations of FAnisotropy.

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3. EXPERIMENTAL SECTION 3.1. Device Fabrication. We present two techniques for surface chemistry modification. One device has a chemically patterned surface of TMS (53° air−water contact angle) and dodecanethiol (104° air− water contact angle) SAM. The other has a TMS and FOTS (108° air−water contact angle) patterned surface. For both processes, the silicon wafer was rinsed with acetone, isopropanol, and deionized water. The wafer was then coated with a liquid film of hexamethyldisilazane adhesion primer and allowed to react for 20 s before being spun dry. The result is a monolayer of TMS on the wafer surface. Photolithography was then performed with 1.2 μm of AZ1512 photoresist. After development, the remaining photoresist forms the pattern of the ratchet’s rungs. An oxygen plasma treatment at 40 W for 5 min removes the exposed TMS (the area not covered with photoresist), revealing a bare silicon oxide layer. At this point, the fabrication sequences of the two devices diverge. For the TMS−FOTS ratchet, the next step was a chemical vapor deposition of FOTS in a standard desiccator using a house vacuum for 1 h. Afterward, the FOTS was annealed by placing the device on a hot plate for 1 h at 150 °C to create covalent siloxane bonds. In the final step, the photoresist was removed with acetone revealing a TMS− FOTS pattern. For the TMS−dodecanethiol ratchet, the next step was an evaporation of 50 nm Au onto the surface, with a 10 nm Cr adhesion layer. Liftoff was then performed. The device was then immersed into a 1:4 dodecanethiol/ethanol (by volume) bath for 1 h to allow for dodecanethiol to assemble on the Au surface. 3.2. Experimental Setup. The experimental setup consisted of an Agilent 33120A function/arbitrary waveform generator, Brüel and Kjær type 2718 power amplifier, Brüel and Kjær type 4809 vibration exciter, Agilent Infiniium oscilloscope, Polytec OFV vibrometer, DRS Data and Imaging Systems, Inc. Lightning RTD high-speed camera, and Matlab on a Windows PC. A die with the wetting barrier ratchet was attached on the vibration exciter such that the die was horizontal and the vibration acted in the vertical direction. Drops of deionized water were pipetted onto the ratchet.

4. RESULTS AND DISCUSSION 4.1. Drop Transport. A 12.5 μL drop on the TMS−FOTS ratchet was transported at 5.4 mm/s when agitated with a vibrational amplitude of 100 μm at 72 Hz. A high-speed camera captured the silhouette of the drop at 1 ms intervals, and several frames from one period of oscillation are displayed in Figure 2A (see the Supporting Information for videos of drop transport). The contact angle was measured for eight stage vibration cycles, and the average and standard deviation for each time point were determined (Figure 2B). Drop transport can be broken down into two distinct phases: footprint expansion and contraction. In the expansion phase, the accelerating stage causes the footprint to expand, effectively increasing the interfacial energy of the drop. Because of the asymmetric pinning of the rungs at the TPL, the leading and trailing edges move differently, expanding 118 ± 34 and 397 ± 41 μm, respectively. In the contraction phase, the TPL of the drop recedes to minimize its interfacial energy. Similar to expansion, recession proceeds asymmetrically with the leading and trailing edges receding 58 ± 34 and 455 ± 25 μm, respectively. The key to drop transport is that the difference in leading and trailing edge recession is greater than the difference in leading and trailing edge expansion.10 Therefore, in one vibrational cycle, the drop is transported on average 60 μm in the direction of the leading edge. 4.2. Actuation Amplitude. The minimum amplitude required to initiate transport, defined as the actuation amplitude, is limited by the pinning at the leading edge. Agitation must be significant enough to advance the leading

Figure 2. Directed transportation of a 12.5 μL drop on a TMS−FOTS wetting barrier ratchet is captured by a high-speed camera as it moves from left to right with a velocity of 5.4 mm/s. Transport is actuated with a vibrational amplitude of 100 μm at 72 Hz. (A) Four frames from one period of oscillation are displayed, and (B) mean contact angles over eight periods are measured and plotted versus time (the standard deviation at each time point is indicated). At 0 ms, the footprint of the drop is at its maximum expansion just prior to recession. Initially, the edge of the drop recedes symmetrically from 0 to 7 ms. Asymmetric pinning is clearly visible from 7 to 9 ms, where the leading right edge of the drop pins to the surface, while its contact angle decreases; simultaneously, the contact angle of the trailing left edge increases as it recedes, leaving a faint residue of water behind. See the Supporting Information for videos of drop transport.

edge of the drop by at least one rung before transport can take place. A geometric sharp edge, i.e., a discontinuity between solid and vapor, will, in general, result in stronger pinning than a chemical edge, i.e., a discontinuity between two surfaces with different wetting properties. Therefore, wetting barrier ratchets are expected to have lower actuation amplitudes than texture ratchets. Actuation amplitudes were measured on texture ratchets versus the two new wetting barrier ratchets with identical rung layouts. The results shown in Figure 3 demonstrate that actuation amplitudes are significantly reduced on both wetting barrier ratchet designs. The most significant 13767

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4.3. Slip Test. To evaluate experimentally how rung curvature affects pinning anisotropy, a slip test was performed.29−31 A drop was placed on a TMS−FOTS ratchet mounted on a horizontal stage. The stage was slowly tilted upward until a critical stage angle (α) was reached, at which point the drop slid downhill off the substrate. The slip test was conducted for three rung radii: 590, 1000, and 1500 μm. Experimental results are shown in Figure 4 for drops ranging in volume from 15 to 30 μL. The critical stage angle varies depending upon the rung orientation (curvature pointing uphill or downhill). Both orientations were tested to find the force of anisotropy. To measure FAnisotropy, the difference is taken between Fslip,uphill and Fslip,downhill in eq 5 FAnisotropy = mg(sin αuphill − sin αdownhill)

(5)

where m, g, αuphill, and αdownhill are the mass of the drop, acceleration due to gravity, and critical stage angles for when rung curvature was pointed uphill or downhill, respectively. The difference in α, displayed in Figure 4B, was largest for smaller radii and decreased as the radii increased. At 30 μL, Δα converged for all ratchets to 8°. The convergence at high volumes can be explained as an indifference to rung curvature when the radius of the footprint was significantly greater than the rung radius. For a 15 μL drop, FAnisotropy was 36.4 ± 1.8, 27.4 ± 1.7, and 3.8 ± 2.6 μN for the 590, 1000, and 1500 μm radii devices, respectively, demonstrating the increased anisotropy for the tested ratchets with smaller rung radii and indicating that they should have superior ratcheting performance. 4.4. Ratchet Performance versus Rung Curvature. As predicted by the slip test, the TMS−FOTS ratchet with a 590 μm rung radius outperformed the others in terms of minimizing

Figure 3. Wetting barrier ratchets reduce actuation amplitudes required to initiate transport in comparison to the previously reported texture ratchet.10 Each device had identical rung layout and was actuated at its resonant frequency for the given ratchet and drop volume. They are listed in order of increasing volume (5, 7.5, 10, 12.5, and 15 μL): texture ratchet (75, 60, 50, 45, and 42 Hz), TMS−FOTS ratchet (115, 95, 82, 72, and 65 Hz), and TMS−dodecanethiol ratchet (97, 85, 74, 67, and 61 Hz). The FOTS design clearly outperformed both the texture ratchet and the dodecanethiol design. Error bars indicate the standard deviation of each set of measurements.

decrease was observed with a 10 μL drop, with a reduction of actuation amplitude from 133 ± 7.5 μm on the texture ratchets to 37 ± 2.3 μm on the TMS−FOTS ratchet. The TMS−FOTS ratchet performed slightly better than the TMS−dodecanethiol ratchet; this is not unexpected, because the 60 nm Au/Cr layer should increase pinning for the leading edge.

Figure 4. Slip test was used to determine the pinning forces for three ratchet designs with rung radii of 590, 1000, and 1500 μm, for drop volumes ranging from 15 to 30 μL. (A) Critical stage angle, α, for each track design is plotted for the rung curvature pointing uphill and downhill, respectively. (B) Difference in α for the rung curvature uphill and downhill experiment is plotted for each track design. (C) Pinning anisotropy (eq 5) was plotted for each track design. The 590 μm device, complete semi-circle, demonstrated the strongest anisotropy. 13768

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comprehensive study directly investigating the issue of boundary curvature and pinning. Several independent investigations have been conducted on the two extremes: circular hydrophilic domain (high curvature) and straight hydrophilic stripe (no curvature). For the circular hydrophilic domain case, TPL advancement occurred when θb = θ2.17,28 In the hydrophilic stripe case,32,33 TPL advancement was observed at θb < θ2. While a more extensive study is required to fully understand the role of boundary curvature in pinning, these studies support our experimental observations that a higher rung curvature increases pinning anisotropy and ratchet performance.

actuation amplitude and maximizing transport velocity. Actuation amplitudes were evaluated over the same set of devices with their results from the slip test for 15 and 20 μL drops in Figure 5. For a 15 μL drop, actuation amplitudes were

5. CONCLUSION We realize a novel DMF platform. The wetting barrier ratchet implements a purely chemical pawl made of periodic semicircular hydrophilic rungs on a hydrophobic background. Wetting barrier ratchets reduce the actuation amplitudes of previously reported texture ratchets more than 3-fold for a 10 μL drop. They can be optically flat, making fully transparent devices possible. The chemical pattern can be simply fabricated in a number of ways, including techniques compatible with cheap mass production (e.g., inkjet or contact printing). The flat surface is easily cleaned, integrated with electrodes and sensors, and compatible for down-scaling to nanoscale features for improved performance. For the first time, we use the line fraction CB equation to provide a theoretical foundation for describing how periodic curved rungs induce anisotropic contact angle hysteresis and drop transport. Experimentally determined pinning anisotropy is shown to be positively related to ratcheting performance in terms of minimizing the actuation amplitude while maximizing transport velocities. For the smallest rung radius investigated, 590 μm, a complete semi-circle had the best ratcheting performance. The wetting barrier ratchet provides a simple and cheap platform for performing drop-based chemical or biological microfluidic functions. It could be implemented in a low-power DMF point-of-care technology or alternatively as a laboratory tool easily integrated with inverted microscopy because of its transparency. Other potential applications include condensation collection on windows or for applications in cooling or desalination.

Figure 5. Actuation amplitudes for three track designs were compared to FAnisotropy measured in the slip test for 15 and 20 μL drops at 74 and 66 Hz, respectively. (A) As the rung radius decreases from 1500 to 590 μm, the actuation amplitude decreases by factors of 2 or 2.8 and FAnisotropy increases by factors of 9.5 or 2.8 for the 15 or 20 μL volume, respectively. (B) At actuation, the drop velocity is faster on the smaller rung radius, despite the lower actuation amplitude. The horizontal line of the cross represents the standard deviation for FAnisotropy, while the vertical line of the cross represents the standard deviation for the actuation amplitude or velocity.

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ASSOCIATED CONTENT

S Supporting Information *

Two AVI videos of the drop transport discussed in Figure 2, with the first being in real time (video length, 0.79 s; ∼55 stage cycles) and the second being in 1/100 of real time (video length, 79.1 s; ∼55 stage cycles). This material is available free of charge via the Internet at http://pubs.acs.org.

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found to be 79.5 ± 1.3, 108.0 ± 6.0, and 158.3 ± 3.4 μm for the 590, 1000, and 1500 μm devices, respectively. Not only did smaller rung radii result in transport at lower actuation amplitudes, but even at lower actuation amplitudes, drops were transported faster. Velocities at actuation were measured to be 4.22 ± 0.15, 2.4 ± 0.08, and 1.98 ± 0.04 mm/s for the 590, 1000, and 1500 μm radii, respectively. The increased force of anisotropy and improved ratchet performance for devices with shorter rung radii suggest a relationship between boundary morphology and pinning strength. To our knowledge, there has not been a

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Present Address

† University of California, Berkeley/University of California, San Francisco Joint Graduate Group in Bioengineering, Berkeley, California 94720, United States.

Notes

The authors declare no competing financial interest. 13769

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(19) Cassie, A. B. D.; Baxter, S. Wettability of porous surfaces. Trans. Faraday Soc. 1944, 40, 546−551. (20) Masao, I. Contact angle hysteresis of cylindrical drops on chemically heterogeneous striped surfaces. J. Colloid Interface Sci. 2006, 297 (2), 772−777. (21) Woodward, J. T.; Gwin, H.; Schwartz, D. K. Contact angles on surfaces with mesoscopic chemical heterogeneity. Langmuir 2000, 16 (6), 2957−2961. (22) Cubaud, T.; Fermigier, M. Advancing contact lines on chemically patterned surfaces. J. Colloid Interface Sci. 2004, 269, 171−177. (23) Larsen, S. T.; Taboryski, R. A Cassie-like law using triple phase boundary line fractions for faceted droplets on chemically heterogeneous surfaces. Langmuir 2009, 25, 1282−1284. (24) Choi, W.; Tuteja, A.; Mabry, J. M.; Cohen, R. E.; McKinley, G. H. A modified Cassie−Baxter relationship to explain contact angle hysteresis and anisotropy on non-wetting textured surfaces. J. Colloid Interface Sci. 2009, 339, 208−216. (25) Hey, M. J.; Kingston, J. G. The apparent contact angle for a nearly spherical drop on a heterogeneous surface. Chem. Phys. Lett. 2007, 447, 44−48. (26) Gao, L.; McCarthy, T. J. How Wenzel and Cassie were wrong. Langmuir 2007, 23, 3762−3765. (27) Nosonovsky, M. On the range of applicability of the Wenzel and Cassie equations. Langmuir 2007, 23, 19919−9920. (28) Blecua, P.; Lipowsky, R.; Kierfeld, J. Line tension effects for liquid droplets on circular surface domains. Langmuir 2006, 22, 11041−11059. (29) Barahman, M.; Lyons, A. M. Ratchetlike slip angle anisotropy on printed superhydrophobic surfaces. Langmuir 2011, 27, 9902−9909. (30) Extrand, C. W.; Gent, A. N. Retention of liquid drops by solid surfaces. J. Colloid Interface Sci. 1990, 138, 431−442. (31) Furmidge, C. G. L. Studies at phase interfaces. I. The sliding of liquid drops on solid surfaces and a theory for spray retention. J. Colloid Sci. 1962, 17, 309−324. (32) Brinkmann, M.; Lipowsky, R. Wetting morphologies on substrates with striped surface domains. J. Appl. Phys. 2002, 92, 4296. (33) Gau, H.; Herminghaus, S.; Lenz, P.; Lipowsky, R. Liquid morphologies on structured surfaces: From microchannels to microchips. Science 1999, 283, 46−49.

ACKNOWLEDGMENTS This work was supported in part by the University of Washington Technology Gap Innovation Fund (TGIF) and in part by a Research Experience for Undergraduates (REU) Supplement to National Science Foundation (NSF) Grant ECCS-05-01628 (Rajinder Khosla, Program Director). Todd A. Duncombe and James F. Parsons received support from the Mary Gates Fellowship. Todd A. Duncombe was also supported by a Washington Research Foundation/NASA Space Consortium Fellowship. The devices described in this work were fabricated at the University of Washington NanoTech User Facility, a member of the NSF National Nanotechnology Infrastructure Network (NNIN).

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ABBREVIATIONS USED DMF, digital microfluidics; CB, Cassie−Baxter; SAM, selfassembled monolayer; TPL, triple line; TMS, trimethylsilanol; FOTS, perfluorooctyltrichlorosilane

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REFERENCES

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