controlling liquid drops with texture ratchets
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Todd A. Duncombe, E. Yegân Erdem, Ashutosh Shastry, Rajashree Baskaran, and Karl F. Böhringer*
Controlling Liquid Drops with Texture Ratchets
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A texture ratchet is a surface region whose microstructured,asymmetric features propel drops when vibrated. Drop motion can persist over long distances, along circular paths, up- or down-hill. Specific drop volumes resonate at specific frequen-cies, providing a means to separately control the motion of different-sized drops. We analyze the physical mechanism responsible for drop transport and reveal the relationship between design parameters such as microscale geometry and surface wettability, operation parameters such as drop volume and viscosity, vibration frequency and amplitude, and perform-ance parameters such as drop velocity. Experiments demon-strate water drop transport on silicon and elastomer substrates. Texture ratchets can move liquid samples without electric fields, pressure gradients or gravity, making them an attractive low-cost platform for lab-on-chip applications.
Microfluidic devices perform physical, chemical, and biolog-ical functions on miniature lab-on-chip platforms, which have appeared in response to the growing demand for portable, fast, safe, and low-cost bioanalysis tools. Often, samples are directed through micromachined elements such as valves, filters and
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T. A. Duncombe[+,†]
Department of Electrical EngineeringUniversity of WashingtonBox 352500, Seattle, WA 98195-2500, USAE. Y. Erdem[+,‡]
Department of Mechanical EngineeringUniversity of WashingtonBox 352500, Seattle, WA 98195-2500, USADr. A. Shastry[+,§]
Department of Electrical EngineeringUniversity of WashingtonBox 352500, Seattle, WA 98195-2500, USADr. R. BaskaranComponents ResearchIntel Corporation, Hillsboro, OR, USAProf. Dr. K. F. Böhringer University of WashingtonDepartments of Electrical Engineering and BioengineeringBox 352500, Seattle, WA 98195-2500, USAE-mail: [email protected][+] T.A.D, E.Y.E., and A.S. contributed equally to this work; they are listed in alphabetical order. [†] Present address: UC Berkeley, UCB-UCSF Graduate Program in Bioengineering, Berkeley, CA, USA[‡] Present address: UC Berkeley, Department of Mechanical Engineering, Berkeley, CA, USA[§] Present address: Corium International, Menlo Park, CA, USA
DOI: 10.1002/adma.201104446
pumps via continuous flow. Drop-based systems present an alternative approach that separates samples into discrete vol-umes, thereby tackling two key challenges in microfluidics: cross-contamination between samples and dilution by diffusion. Liquid transport can be effected by gradients, for example in con-tinuous microfluidics via pressure-driven or electrokinetic flow, or in discrete microfluidics via thermocapillary actuation,[1–3] electrowetting,[4–6] or chemical gradients[7–9] that also include instances where drops travel on inclined, curved or upside-down surfaces.[7–10] Surface energy gradients can also be pro-duced by chemically homogeneous but microscopically textured surfaces that transport drops across short distances.[11] Here, we introduce texture ratchets–substrates that result in asymmetric pinning forces along the three-phase contact line of a drop: under vertical vibration, the drop experiences a net force that controllably propels it along the horizontal surface (Figure 1). Using this idea, we have built devices in which microliter-sized drops follow predetermined tracks of arbitrary lengths and shapes. The amplitude of vibration of the substrate that is required to initiate motion is lowest at the resonance frequency of a drop, which increases with surface tension and decreases with drop volume and viscosity.[12,13] Consequently, we dem-onstrate that motion of individual drops can be discriminated by their volume and viscosity, providing a simple addressing scheme when multiple drops are present in the device.
Ratchets are devices that generate directed motion. While extensively studied for delivery of solid objects in industrial parts feeders,[14,15] more recently reported ratchets have uti-lized saw-tooth geometries[16–18] and vibrations[19,20] or ani-sotropic nanostructures[21,22] to induce asymmetry for liquid transport. The reported transport mechanisms vary widely, with examples including acoustic vibrations,[22,23] electrowetting,[16] superparamagnetism,[17] and the Leidenfrost effect.[18] Texture ratchets, first described by Shastry et al.,[23] direct sessile drops in “fakir” state[24–26] along a track when subjected to vibra-tion. Fakir drops are able to sustain high pressure,[27] allowing them to be strongly vibrated without risking transition to the surface-conforming Wenzel state. Sparse pillars on either side of the ratchet track create a potential well that keeps the drops confined to the track. When the track is subjected to vertical sinusoidal vibration, the three-phase contact line forming the footprint of the drop moves–alternately undergoing advancing (wetting) and receding (dewetting) motion. The texture ratchet exploits two sources of asymmetry to translate these seemingly random oscillations of the contact line into a net movement of the drop: (1) A longer three-phase contact line conforming with the arced rung at the leading edge produces a higher pinning force. (2) Wetting in general is less sensitive to texture than dewetting.[28]
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Figure 1. The texture ratchet. (A) A sessile water drop with 20 μL volume on a texture ratchet composed of a series of arced rungs and delimited by pillars. (B) Scanning electron micrograph of a texture ratchet; it is etched in silicon and coated with fluoro-octyl-trichloro-silane (FOTS). We have also molded texture ratchets in elastomers. The image shows a partial view of the arced rungs and the adjacent pillar arrays that form a microscopically rough superhydrophobic surface. (C) Schematic top view of the interaction between drop and ratchet during vibration: (i) The footprint of the drop aligns with an arced rung along its leading edge, while its trailing edge crosses several rungs. (ii) The footprint of the drop expands as the ratchet accelerates upwards during vibration. (iii) The footprint of the drop contracts as the ratchet accelerates downwards during vibration. (iv) After one oscillation cycle, the drop has moved towards the right.
We attached a texture ratchet on a level stage mounted on an electromagnetic linear motor, which was connected to a function generator via an amplifier (see Experimental Section). Vibrating the stage vertically produced horizontal drop move-ment. In our first set of experiments, we operated the stage at the resonance frequency of the drop (55 Hz for an 8 μL drop) using the minimum stage amplitude (0.2 mm) that resulted in movement. We captured the drop silhouette with a high-speed camera and analyzed it with automated image processing soft-ware, recording drop position and contact angles as a function of time (Figure 2 and Supporting Information, Video S1). The stage vibration caused cyclic oscillations of the drop, leading to periodic expansion and recession of the drop footprint. Figure 2A shows the drop silhouette taken at 6 ms intervals. Automated tracking data of the leading edge, trailing edge, centroid and contact angles are plotted in Figure 2B, with an average velocity of the drop centroid of 11.5 mm/s. In addi-tional experiments, we observed velocities from less than 1 mm/s to greater than 25 mm/s, depending on the particular track design, vibration amplitude and frequency, as well as drop volume, density and viscosity. Increasing amplitudes generally led to faster velocities until excessive vibrations tossed the drops from the ratchet track.
To reveal the working principle of the texture ratchet, we start with a simple thought experiment: a drop sits on a hydrophobic substrate that oscillates in the vertical direction with a sinu-soidal displacement. In response, the drop oscillates between an elongated and a compressed shape (similar to Figure 2A). This forced oscillation is strongest at the resonance frequency of the drop. For small agitation amplitudes, the contact line remains pinned on the substrate due to contact angle hysteresis.
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Above a threshold amplitude, the contact line de-pins and the footprint of the drop advances and recedes during each oscil-lation period. On a perfectly isotropic horizontal surface, this oscillation is symmetric and the center of mass does not move horizontally. However, for our experiments we have created ani-sotropic surfaces where the de-pinning forces are asymmetric: the semi-circular rungs provide continuous pinning of the drop footprint along its leading edge but only intermittent pin-ning along its trailing edge; therefore, the advancing angle at the leading edge is larger than at the trailing edge (θLA > θTA) while the receding angle at the leading edge is smaller than at the trailing edge (θLR < θTR). Furthermore, receding contact angles differ more than advancing contact angles (|θLR – θTR| > |θLA – θTA|), as previously noted by Shastry et al.[11] for sur-face energy gradients and again observed in our experiments (Figure 2B). Consequently, the drop experiences a net forward force during dewetting and a net backward force during wet-ting. Over one oscillation period, the effect of this force does not necessarily sum to zero, as shown by Noblin et al.[29] They applied sinusoidal forces on a drop simultaneously in hori-zontal and vertical directions, and the drop responded with a ratcheting motion–unless vertical and horizontal forces were of equal magnitude and phase. Unlike Noblin’s system, our device only applies periodic vertical force but the anisotropic surface “rectifies” it into a horizontal force component. Thus, a texture ratchet under vertical agitation can induce controlled motion in a drop. To propel a drop with volume V, we vibrate the system at (or near) its resonance frequency fV. The velocity v of the drop is the product of fV, rung spacing s, and the number n of ratchet rungs over which the drop passes in one oscillation: v = n s fV. With good approximation, fV and thus v are proportional to
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Figure 2. Drop transport on a texture ratchet. (A) Snapshots of an 8 μL water drop taken with the high-speed camera at 6 ms intervals, captured as silhouettes on a screen. Taken from Video S1. (B) Image processing software tracks the apex of the leading edge (xL), the apex of the trailing edge (xT), the centroid (xC) and the leading and trailing contact angles (θL and θT) over time; the cyclic displacement of the stage (yS) at 55 Hz is also captured. Fourier analysis of the drop motion shows that the 4th order Fourier series (frequency cut-off above 220 Hz) produces a tight match with the experi-mental data (continuous red lines for xL, xC, and xT). Note: Displayed θL and θT data were smoothed by a two-point moving average.
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Figure 3. Selective transport of drops with different volumes and viscosities. (A-B) Experimentally determined acceleration a at which the drop starts to move on the ratchet versus the driving frequency f for various volumes and viscosities. The letters a-g indicate the parameter sets used for selective transport in panels C-F. (A) The frequency-acceleration map for different volumes. (B) The frequency-acceleration map for liquids with different viscosi-ties. (C) The 5 μL drop is transported with parameter set a while the 8 μL drop is stationary. When the two drops merge, the resulting 13 μL drop is transported with parameter set b (Video S2). (D) The 8 μL drop is transported with parameter set c while the 5 μL drop is stationary. After merging, parameter set d transports the resulting drop (Video S3). (E) The simultaneous transport of 5 μL and 8 μL water drops on two opposing ratchet tracks. Driving parameters are selected from the region where the mappings of each drop intersect. Parameter set e is used (Video S4). (F) The selective motion shown for drops of different viscosities. The 8 μL water drop is transported with parameter set f. When it merges with the 8 μL 50% (v/v) glycerol-water mixture, the resulting drop is transported with parameter set g (Video S5). Note: The three response curves in (A) will overlap almost perfectly if the frequency and acceleration data are normalized. For a drop of volume V, normalizing the frequency means dividing by the resonance frequency, which is approximately proportional to V−½; normalizing the acceleration means factoring out inertia, which is proportional to V (see Daniel et al.[19] for an analogous analysis). Scale bars: 1 mm.
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V , where γ is the surface tension of the liquid.[12,13] Typically, n is a small number but not necessarily 1, and it may fluctuate over time. In the experiment in Figure 2, we observed n = 2 for 20% and n = 3 for 80% of oscillation cycles, resulting in a drop velocity v = 2.8 · 75 μm · 55 Hz = 11.5 mm/s. Currently, no analytical model exists to determine n; it derives from the time-varying lateral forces that ensue along the moving contact line, which in turn are dependent on design parameters such as cur-vature, width and spacing of rungs plus the intrinsic contact angle of their surface material. A comprehensive model could combine Noblin’s approach[29] with Mettu and Chaudhury’s analysis[20] to capture the coupling between normal and lateral oscillations of the drop.
The mapping between drive amplitude and frequency for different volumes and viscosities is shown in Figure 3A,B. Drops with smaller volumes and higher viscosity require larger accelerations due to the reduced inertia and increased
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damping, respectively. Drops of different volume or viscosity can be moved simultaneously when the system is driven with parameters from the overlapping regions whereas a single one of them can be transported with parameters from the non-over-lapping regions, offering the ability to address individual drops. Figure 3C–F and Supporting Information, Videos S2-S5 show programmed transport of drops by volume or viscosity either simultaneously or sequentially. Drops of different properties are colored with water soluble red and blue inks.
Ratchet tracks have transported drops in linear and closed circular as well as in upside-down configurations. Circular tracks (Figure 4A and Supporting Information, Video S6) dem-onstrate several key attributes of texture ratchets, including the capability of simultaneously propelling different drops over long distances and without energy gradients. Curved tracks differ from straight tracks by a reduced range of the effective frequency and amplitude to achieve drop movement, as well as
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Figure 4. Circular and upside-down drop transport. (A) The blue water drop (volume 22 μL) sits on the one-inch-diameter circular track and the red drop (volume 20 μL) sits on the two- inch-diameter circular track of a silicon/FOTS texture ratchet. The frequency of the stage is 41 Hz. The blue drop travels with an average speed of 1.5 cm/s, corresponding to an angular speed of 1.2 rad/s and a cycle period of 5.4 s. The red drop travels with an average speed of 2.2 cm/s, corresponding to an angular speed of 0.88 rad/s and a cycle period of 7.1 s (Video S6). (B) The stroboscopic image depicts two pairs of 5 μL dyed water drops simultaneously traveling and finally merging on regular and upside-down texture ratchets molded in polydimethylsi-loxane (PDMS) elastomer. Each substrate has two opposing ratchet tracks (same as in Figure 3E). The parameters of actuation are 75 Hz and 10.4 g (see also Video S7).
a higher sensitivity to a tilted stage. In one instance, a drop continuously moved for 25 min on a track with a 2.5 cm radius; we adjusted the frequency of the stage as evapo-ration gradually reduced the drop’s volume from approximately 22 μL to 4 μL. Upside-down motion of drops illustrates that orien-tation with respect to gravity is not critical for transportation (Supporting Information, Video S7). Figure 4B shows two sessile and two pendant drops being transported on ratchet tracks that are attached back to back. The acceleration required for the upside-down motion is higher than for the sessile drop motion. Hence the sessile drops move faster than the pendant drops as the system is driven by parameters to transport all drops simultaneously. Transportation on curved and uphill surfaces was also successful (Sup-porting Information, Videos S8, S9).
The long-term goal of microfluidic lab- on-chip technology is a reliable, self-contained system that maximizes efficiency and throughput in chemical or biomedical proc-esses while reducing the cost, size and number of system components. Texture ratchets have the potential to serve this pur-pose: Many drops can be transported simul-taneously on a vibrating substrate, requiring only modest manufacturing costs and little applied energy. Texture ratchets, as opposed to energy gradients, can sustain drop trans-port over long distances and periods of time, including closed paths. A global energy input to the system via vibration leads to locally controlled transport of individual drops. Since lithography rather than self-assembly defines the texture ratchet, it can be designed with spatially varying features that influence the motion of a drop, including direction and speed; in addition, we expect that finer texture (nano-scale instead of micro-scale) will pro-duce smoother transport at lower vibration amplitudes. The most closely related “device” may be the beak of phalaropes and other shorebirds, which transport liquid by repeat-edly squeezing a drop between the upper and lower jaw, creating a capillary ratchet;[30] in contrast, a texture ratchet requires only one surface. Compared to electrowetting-on-die-lectric, texture ratchets are not restrained by the conductive or dielectric properties of the drop (although they are restricted by surface tension) and there is no possibility of dam-aging biomolecules or cells with high electric fields. Different materials and configurations demonstrate the versatility of texture ratchets for portable devices. The possibility to acti-vate texture ratchets by random oscillations
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may provide the opportunity to harvest naturally occurringvibrations for drop transport, for example in moving vehicles or in hand-held or wearable devices.
Experimental SectionTo fabricate the silicon ratchets, we patterned a silicon wafer by optical lithography before performing a Bosch deep reactive ion enhanced (DRIE) etch to a depth of 40 μm. We activated the wafer with “piranha” (a cleaning solution consisting of sulfuric acid and hydrogen peroxide) and vapor-coated it with fluoro-octyl-trichloro-silane (FOTS, Sigma Aldrich). To fabricate the elastomer ratchets, we created a 60-μm thick master mold with SU8-2050 (MicroChem Corporation) by optical lithography. We silanized the master mold, poured approximately 5 mm of polydimethylsiloxane (PDMS, Sylgard 184 Silicone Elastomer Kit) over it and cured it at 70 °C for one hour. The experimental setup consisted of an Agilent 33120A function/arbitrary waveform generator, Brüel & Kjær Type 2718 power amplifier, Brüel & Kjær Type 4809 vibration exciter, Agilent Infiniium oscilloscope, Polytec OFV vibrometer, DRS Data & Imaging Systems Inc. Lightning RTD high-speed camera and Matlab on Windows PC.
Supporting InformationSupporting Information is available from the Wiley Online Library or from the author.
AcknowledgementsThis work was supported in part by Intel Corporation, NIH Center for Excellence in Genomic Science 5-P50-HG002360-06, NSF IREE grant ECCS-05-01628, REU supplement to NSF NIRT grant CMMI-0709131 and University of Washington Technology Gap Innovation Fund 2-60-00-07-49-0. T.A.D. received support from a Mary Gates Fellowship and a Washington Research Foundation / NASA Space Consortium Fellowship. We thank Marianne Case, Ji Hao Hoo, Ahlmahz Negash, Sangjun Park, James Parsons, Aimi Ahmad-Shukri, Dane Taylor and Genevieve Vigil for their help in the laboratory; Michael Isaacs for taking stroboscopic images of drop transport; Daniel Gottschling, Jerry Pollack, Buddy Ratner and Paul Yager for valuable comments on this manuscript; Hiroyuki Fujita and his group at the University of Tokyo for hosting and supporting K.F.B. and T.A.D.; and the staff and users of the NSF NNIN Nanotechnology User Facility and the Microfabrication Facility at the University of Washington for their support.
Received: November 21, 2011 Revised: December 28, 2011
Published online: February 14, 2012
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