Acoustically driven programmable liquid motion using resonance cavities

Abstract

Performance and utility of microfluidic systems are often overshadowed by the difficulties and costs associated with operation and control. As a step toward the development of a more efficient platform for microfluidic control, we present a distributed pressure generation scheme whereby independently tunable pressure sources can be simultaneously controlled by using a single acoustic source. We demonstrate how this scheme can be used to perform precise droplet positioning as well as merging, splitting, and sorting within open microfluidic networks. We further show how this scheme can be implemented for control of continuous-flow systems, specifically for generation of acoustically tunable liquid gradients. Device operation hinges on a resonance-decoding and rectification mechanism by which the frequency content in a composite acoustic input is decomposed into multiple independently buffered output pressures. The device consists of a bank of 4 uniquely tuned resonance cavities (404, 484, 532, and 654 Hz), each being responsible for the actuation of a single droplet, 4 identical flow-rectification structures, and a single acoustic source. Cavities selectively amplify resonant tones in the input signal, resulting in highly elevated local cavity pressures. Fluidic-rectification structures then serve to convert the elevated oscillating cavity pressures into unidirectional flows. The resulting pressure gradients, which are used to manipulate fluids in a microdevice, are tunable over a range of ≈0–200 Pa with a control resolution of 10 Pa.

Microfluidic systems continue to rely on externally applied pressures for the manipulation of fluid samples. As such, operation of a chip can often require extensive off-chip control equipment. Syringe pumps (displacement pumps), for instance, although ideal for continuous-flow applications such as organic/particle synthesis (1–4), and droplet generation (5) are impractical for control of complex microfluidic devices because each fluid input requires a dedicated pump. Manipulation of discrete fluid droplets, on the other hand, is typically accomplished by using air pressure (6). However, careful attention needs to be paid to the magnitude of the pressure gradient (7) because most bench scale regulators are not designed to produce the minute pressure differences needed for precise droplet control.

Many researchers introduce pressure-attenuation mechanisms to circumvent large and undesirable pressure gradients. For example, Pal et al. (8) used intermittent pulsing of a coarsely regulated pressure source to precisely position drops. Reciprocating displacement micropumps constitute a popular choice for on-chip pressure generation (9). These pumps operate by pairing the displacement of a diaphragm, typically driven piezoelectrically, with some form of rectification structure. But despite the remarkable performance of these and other on-chip pressure sources, they possess many of the same limitations as their macroscopic counterparts. Chang et al. (10) report on an approach to distributed pressure control using microfabricated Venturi nozzles, whereby coarsely regulated air pressure is converted into pressures better suited for droplet control. Hybrid schemes employing both displacement and direct pressure are also possible, most notably, for serial deflection of elastomeric membranes (11). But despite multiplexing efforts aimed at reducing the number of external control variables (12), the number of off-chip connections and control equipment necessary to operate a reasonably complex device can remain prohibitively large.

Apart from conventional pressure-driven mechanisms, on-chip acoustic-based methods for fluidic actuation are becoming increasingly common in areas ranging from fluid transport (13, 14), mixing (15), and separations (16) to droplet sequestration (17). Acoustic streaming, also known as quartz wind, is a phenomenon by which steady momentum flux is imparted to a fluid by the impingement of high-amplitude acoustic waves. Bulk fluid motion can result from the build up of a nonlinear viscous Reynolds stress at the incident fluid boundary (18). Microfluidic applications using acoustic streaming have thus far been limited primarily to driving closed-loop fluid circuits (19, 20) mainly because of extremely low back-pressure tolerance on the order of 1 Pa. Surface acoustic wave (SAW) devices also use acoustic streaming but operate on open planar surfaces rather than within closed channels. SAWs can be launched in piezoelectric substrates by application of resonant frequencies to sets of interdigitated electrodes, with the resonant frequencies determined by electrode spacing. SAWs, in conjunction with hydrophobically altered surfaces, are attractive for microfluidic control because droplets residing in the path of a launched wave undergo a rolling motion due to acoustic streaming at the leading pinned meniscus of the drop. As such, the SAW platform can be used to position droplets arbitrarily along the lines of intersecting electrode paths.

We have devised a distributed pressure-control scheme that employs acoustic resonance cavities and rectification structures to translate the frequencies contained in an acoustic signal into separately addressable output pressures that can be used to control liquids in a microfluidic device. Unlike any pressure control scheme we are aware of, the device is capable of simultaneously controlling multiple output pressure signals, in either a pulsed or continuous fashion, over a range of ≈0–200 Pa with a control resolution of 10 Pa. These capabilities eliminate the need for pressure-attenuation mechanisms, reduce external control infrastructure, and greatly improve on the back-pressure tolerance of acoustic streaming-based methods.

Results and Discussion

Operation of a microfluidic device by using musical tones to induce motion is accomplished with a form of pneumatic decoding similar to what occurs in fiber-optic electronic communication. An encoded acoustic signal composed of a specific blend of resonant tones is decoded and transduced into a set of discrete pneumatic signals proportional to the tonal content. This transduction occurs in 2 parts: First, acoustic cavities experience a dramatic increase in sound pressure when exposed to a resonant tone. Second, rectification structures attached to the cavities convert the amplified oscillating pressures into net unidirectional flows. As an example of this transduction, a programmed sequence of musical tones (Fig. 1C, Tone Sequence) was synthesized on a computer and delivered to a bank of 4 resonance cavities (Fig. 1A) with principal resonance modes at 404, 484, 532, and 654 Hz. The outlet flow rate from each cavity was monitored by using a hot-wire anemometer, and, although each cavity is subject to the same input, their output is frequency dependent (Fig. 1C). Specifically, the input sequence, which grows in complexity during the experiment, triggers an output only at the cavities whose resonant tones were present. Fig. 1 also shows that each cavity exhibits a stable and repeatable step-like response to its resonant tone and that the presence of other competing tones produces no spurious output. For the sake of graphical clarity, as well as a demonstration of flow control, the output flow rate of each cavity was set to ≈300 standard cubic centimeters/minute. However, by using the computerized interface linked to the device, it is trivial to adjust the output flow characteristics of any specific cavity simply by adjusting the relative strength of the tone in the input wave form.

Fig. 1.

Resonance-triggered air-flow study. (A) Conceptual representation of the device illustrating key components subject to the same acoustic input. (B) Location of cavity resonance frequencies on the chromatic scale. (C, Tone Sequence) Input acoustic signal represented both graphically and musically by proximity to nearest natural tone on the chromatic scale. (C, bottom) Outlet flow rate as a function of time recorded at the outlets of the 4 rectification structures. Output for each resonance cavity is stable, responsive to a single musical queue, and insensitive to the presence of other competing tones.

Acoustic Resonance.

Perhaps the most intriguing facet of this control scheme is the use of resonance cavities as pneumatic decoders, a concept first explored by Rudolph Koenig (ca. 1880), who used an apparatus comprised of a bank of Helmholtz resonators as a means of dissecting the frequency content of sound. Decoding, in this context, refers to the selective and nondestructive amplification of target frequencies from a complex acoustic excitation. Each of the 4 acoustic cavities in our device, in effect, plucks from the ambient sound field the frequency at which it prefers to oscillate and amplifies that signal, producing a local oscillating cavity pressure significantly greater than that of the incident wave. Amplification in this case occurs because of standing wave resonance (SWR), a phenomenon that describes the addition of an incident wave and its reflections within an acoustic cavity (i.e., the geometry of the cavity is such that incident wave fronts combine perfectly with oppositely traveling reflections). In a so-called “quarter-wavelength” resonator, such as those used here, the principle resonance occurs at a frequency whose quarter wavelength is equal to the axial cavity length. Higher harmonics, in the case of a quarter-wavelength resonator can occur at odd integer multiples of the principle.

Resonance spectrographs (Fig. 2A) were obtained by subjecting the device to a range of frequencies at constant voltage while monitoring outlet flow rate. The emergence of highly elevated peaks in outlet flow corresponds, as mentioned above, to the principal SWR mode of each cavity. Over the frequency domain sampled, each cavity is sympathetic to exactly 1 narrow, nonoverlapping band of frequencies, the width and spacing of which determines, for a limited frequency range, the number of independent pressure outputs that may be controlled. For example, by using an average peak width of 21 ± 10 Hz from Fig. 2 and a frequency range of 808 ± 50 Hz computed as the difference of the first harmonic and the lowest principle (i.e., 1,212 Hz − 404 Hz), the number of cavities and, therefore, signals that can theoretically be controlled is 38 ± 18. However, with improved cavity design, the number of independent signals can be significantly higher than this number.

Fig. 2.

Acoustic resonance performance of the device. (A) acoustic resonance spectrograph representing the acoustic response of each cavity (1–4) subject to a steadily ramped input frequency at constant power. Cavities 1–4 exhibit marked SWR peaks at 404, 484, 532, and 654 Hz, respectively. (B) Two-dimensional FEM simulation result for an arbitrary cavity exhibiting resonance at 860 Hz, illustrating the effect of increased radiation losses on Q for the aspect ratios: 2.3, 4.6, 7.7, 11.5, and 23.

The sharpness of a resonance peak is related to the quality of resonance (Q = the ratio of stored to radiated acoustic energy per cycle). Quantitatively, we can define Q as the resonance frequency divided by the peak band width at half of the maximum value. With respect to the device presented here, cavities with high Q values are preferred as they minimize the required input energy and allow for a greater number of cavities to be situated in a finite frequency domain. To understand the role of our cavity geometry as it pertains to Q, finite element simulations were performed for a simplified 2-dimensional geometry varying the ratio of the cavity diameter to the outlet port diameter. In Fig. 2B, we notice that Q decreases with decreasing aspect ratio, a result consistent with the intuitive suspicion that increases in the relative diameter of a radiation port cause a proportionate increase in radiation loss.

Rectification.

Rectification structures are critical to the working concept of the device. In general, the role of such structures in the context of fluid flow is to introduce a directional bias in the flow, thereby imparting a preferred flow direction from an oscillating input. The bias itself can be implemented by using a moving structure, as in the case of a check or flap valve, or alternatively, by using stationary structures and exploiting a physical property of the working fluid. For an inertial rectifier (21) such as the one we have used here (schematic Inset, Fig. 3) a synthetic jet (22) is used to introduce an asymmetry in the flow leaving the rectifier outlet. During operation, vibrating air within each cavity serves as an oscillating input pressure source to the rectifier. Only under resonant excitation is the pressure gradient of the oscillating flow field of sufficient strength to form a synthetic jet.

Fig. 3.

Rectifier outlet flow subject to ± 0.03 kPa of inlet air pressure. (Left) Experiment showing the resulting rectifier outlet flow rate over a range of inlet pressures. (Inset, plot) Evolution of rectifier flow bias computed as the difference in outlet flow rate at a given pressure swing. Bias at ± 0.02 kPa represented as a pair of squared points. (Inset, schematic) Two-dimensional rectifier geometry used in FEM simulations. (Right) Velocity field snapshots from FEM 2-dimensional incompressible flow simulations. The top 2 images show the reversible viscous dominant flow field for extremely small inlet pressures ±1e-6 kPa. The bottom 2 images show the inertial dominant flow field at a pressure swing of ±0.01 kPa. Marked differences in the velocity field emerge because of flow separation and jetting at the rectifier inlet mouth.

Fig. 3 presents both the experimental and simulated performance of our rectifier when subjected to a steady-state inlet pressure. For a prediction of the asymmetry of an oscillatory input, the flow at equal but opposite input pressures can be compared, and we will use the term “pressure swing” to describe such a pair of pressures. The experimentally obtained flow bias for a pressure swing of 0.01 kPa is illustrated in Fig. 3 by a pair of squared points; the evolution of the bias in the vicinity of zero pressure is shown in the Inset. Finite element method (FEM) simulation results (Fig. 3, vertically tiled images at right) for a simplified 2-dimensional rectifier of the same dimensions reveal that the bias is the result of differences in the velocity field for low and high inlet pressure swings. At low inlet pressure swings (1e-6 kPa), as in the case of the top 2 simulation images, the velocity field is dominated by viscous forces and is thus perfectly reversible. Conversely, for higher inlet pressure swings (1e-2 kPa), as in the case of the bottom 2 images, the velocity field is dominated by inertial forces and is highly asymmetric. Here, when vacuum is applied at the inlet, the resulting velocity field is more or less evenly divided among the 3 remaining ports; however, application of a positive inlet pressure leads to the formation of a synthetic jet that extends from the mouth of the rectifier inlet toward the outlet. Application of a sinusoidally varying inlet pressure of sufficient strength then leads to a net unidirectional flow at the rectifier outlet. Thus, the presence or absence of resonant tones allows us to jump between inertial- and viscous-dominated regimes, thereby precisely controlling the state and level of each cavity output pressure.

Acoustically Driven Liquid Motion.

To illustrate the power of this concept for applications in microfluidic flow control, the device was connected to a polydimethylsiloxane (PDMS) chip with 4 parallel input channels each containing a 3-μL water droplet (Fig. 4A). Prescribed sequences of resonant notes, each being responsible for the actuation of a single drop, were then used to selectively actuate droplets. Droplet velocity in response to the acoustic input signal is shown in Fig. 4B. Acoustic input signals consisting of both single notes and chords produce instantaneous and targeted droplet motion, as shown in Fig. 4B and supporting information (SI) Movie S1. To illustrate the speed at which instructions can be carried out, the tone durations in this experiment were kept brief (≈0.2 s) amounting to droplet displacements on the order of 0.2–0.5 mm per pulse. However, computerized wave-form construction allows for full customization of the tonal input. Thus, a droplet can easily be moved over a longer distance or at a faster pace simply by adjusting the amplitude and duration of the corresponding wave component.

Fig. 4.

Multiplexed droplet motion. (A) Schematic representation of experimental setup depicting an input acoustic signal delivered to an array of resonance cavities, each of which is linked to an input on a microfluidic device (not to scale). (B) Input acoustic signal and resulting droplet velocity as a function of time, illustrating programmed actuation of specific droplets in response to resonant musical tones supplied to the device (see also Movie S1). Chord amplitudes used to produce uniform droplet velocities were: B-C (0.89, 0.85), A-D (0.76, 1.39), A-C-D (0.80, 1.18, 1.25), and A-B-C-D (0.76, 0.76, 0.90, 1.25).

Although equal tone amplitudes of the input wave form do not produce uniform droplet velocities, the amplitude can easily be adjusted to compensate for this effect. In Fig. 4, for example, with the audio amplifier set to output 7.92 V for an input wave amplitude of 1.0 the amplitudes resulting in the uniform movement of droplets A, B, C, and D were: 0.77 (404 Hz), 0.90 (484 Hz), 1.23 (532 Hz), and 1.42 (654 Hz), respectively. Increased voltage was necessary for higher-frequency cavities because speaker displacement and as such, cavity output, is frequency dependent. In addition to the normalization of single tones, amplitudes were also adjusted within chords because early experiments exhibited a systematic enhancement of droplet velocity that appeared to be unique to each chord most likely because of frequency specific wave coherence. Amplitude multipliers unique to each chord were obtained, as in the case of single droplets, by monitoring droplet motion over many chord pulses. Despite efforts to ensure perfectly uniform droplet motion, however, variations of up to 20%, on average, still exist because of fabrication inhomogeneities (Fig. 4B).

To demonstrate the use of this scheme for the operation of more complex systems, the device was used to direct discrete drop motion within a network of pneumatically coupled channels. In contrast to the parallel channel network shown in Fig. 4, a branched network often necessitates the combination of multiple inputs to carry out a specific fluidic operation. Fig. 5 illustrates how the 4 control inputs of the device were used to perform the standard fluidic unit operations of merging, mixing, transport, sorting, and splitting. To ensure precise operation, droplets were actuated in a pulsatile fashion, a strategy that is preferred when maneuvering one or more liquid slugs near a pressure node or junction (see also Movie S2). For example, during the splitting operation shown in Fig. 5, the velocities of the 2 daughter droplets approximately double upon splitting. Use of continuous pressure control in this case would lead to a runaway of the resulting 2 slugs, a problem that is easily circumvented by shortening the time scale of the driving pressure. Conversely, for cases in which pulsatile control is not preferred, such as for droplet transport over long distances or continuous-flow operations, the device output can be readily converted to continuous operation.

Fig. 5.

Performance of standard microfluidic unit operations by using acoustically controlled droplet motion. (Upper Left) Schematic of branched-channel PDMS device with associated cavity linkages. (Upper Right) Channel layout with legend, illustrating the visual representation of 3 pressure states. Main pressure indicates areas where significant pressure is applied to induce droplet motion. Support pressure indicates areas where minimal pressure is applied to counter droplet motion. (Lower) Four sets of images depicting the standard fluidic unit operations of merging, transport, splitting, and sorting. Arrows on each image indicate ensuing droplet motion in response to acoustically generated pressures (linking image)

In additional to propelling individual drops, the system we describe can also be used to pump continuous streams of fluid. Fig. 6 illustrates how the device, when operated in continuous output mode, can be used to generate customizable acoustically switchable concentration gradients (see also Movie S3). In the experiment, dynamically reconfigurable gradients are generated by connecting the device to 4 reservoirs of colored water and altering the strength and tonal composition of the acoustic output. When an acoustic signal is introduced, a gradient rapidly forms with a composition representative of the tones and amplitudes present (Fig. 6, 2–8). For clarity, the output pressure of each cavity was set to the same value (≈100 Pa), however, fine tuning of the component flow ratios is straightforward and involves a simple adjustment of the relative amplitudes of the input tones.

Fig. 6.

Acousticially switchable gradient generation. (Left) Schematic representation of PDMS device used in gradient generation experiments. Resonance cavities are interfaced with the microfluidic device according to the frequencies listed. (Right) A series of images depicting the state of the tonal input (image Inset schematic) and the resulting liquid gradient that is produced. Cavity pressures were all tuned to ≈100 Pa.

Conclusions

This work introduces an acoustic-based approach to distributed pressure control. In a process that can be likened to fiber-optic communication, the device we have fabricated utilizes elements of acoustic resonance, fluidic rectification, and computer control in a simple arrangement to generate multiple independently addressable output pressures in the range of 0–200 Pa (control resolution of ≈10 Pa) that can be operated via a single control line. The device was interfaced to both droplet-based and continuous-flow microfluidic systems and used to carry out various operations such and merging, transport, splitting, sorting, and on-demand gradient generation. Future devices may be scaled down and employ alternative methods of signal generation such as the direct displacement of a sealed cavity by using piezoelectric transducers or noncontact vibration of a flexible membrane by using a remote acoustic source. Development of an on-chip equivalent to the device presented here could greatly simplify operation of complex lab-on-a-chip devices potentially extending the application base of such tools to nonscientists.

Materials and Methods

Device Construction.

Device assembly is schematically represented in Fig. 7. The acoustic source is a standard audio speaker (PDMW6; Pyle). The common air cavity was formed from a 0.155-m segment of 0.152-m i.d. thick-walled Pyrex. The cover plate was fabricated from a 0.155-m-diameter, 0.01-m-thick acrylic sheet. Four, 47-mm i.d. holes, for the cavity mounting ports were drilled in the cover plate along with five 7-mm i.d. vent holes for the minimization of pressure cross-talk (Fig. 7, Cover Plate). Four resonance cavities were formed from 47-mm i.d., 51-mm o.d., borosilicate tube stock cut to 192, 156, 141, and 111 mm. Cavities were sealed at one end, save for a small 2-mm i.d., 6-mm o.d. borosilicate rectifier inlet port. Rectification structures consist of a 2-mm i.d. port that extends slightly into the confluence of a 3-way cross formed by fusing 3 lengths of 4-mm i.d., 6-mm o.d. Pyrex tubing (Fig. 7, Resonance Cavity/Rectifier). All of the components in the final assembled device were bonded by using an off-the-shelf RTV silicone except for the rectification structure that was joined by using a durable epoxy.

Fig. 7.

Device construction. (Upper) Exploded schematic view of device. (Lower) Detail of Cover Plate and Resonance Cavity/Recitifer with dimensions.

Measurement of Cavity Resonance.

A constant voltage analog signal was generated by using Labview (PCI-6031E) and amplified by using a standard audio amplifier (AMP-100; Audiosource). In a typical experiment, the input wave form was steadily ramped from 300 to 800 Hz, and the resulting output flow rate was monitored by using a custom hot-wire anemometer and bridge circuit. Flow measurements were taken by placing the anemometer just in front of the rectifier outlet port and surrounding the assembly with a paper cylinder to minimize disturbance from ambient air currents.

Rectifier Flow Bias.

For positive gauge pressures, air was delivered to the rectifier inlet by using a mass flow controller (11598B-05000SV MKS). Application of negative gauge pressure was performed by using a 2-stage vacuum regulator in conjunction with a house vacuum source. In each case, the inlet pressure was monitored with a strain gauge (DP-25B-S; Omega) extending from a T junction just before the rectifier inlet. Outlet flow rate was monitored by using a custom hot-wire anemometer and bridge circuit.

Programmed Droplet Motion.

Droplet experiments shown in Figs. 4 and 5 were performed by coupling resonance cavity outlets to a nearby PDMS device by using standard silicone tubing and syringe tip connections. The PDMS devices were fabricated by using standard soft-lithography protocols with 1,000-μm-wide by 500-μm-deep channels. PDMS provides an ideal hydrophobic substrate on which to perform these experiments, because the nonwetting properties of the material eliminate the problems of droplet pullback and volume loss that accompany wetting surfaces. Before the experiment, a 3-μL colored water droplet was loaded into each channel by using a micropipette. To induce droplet motion, computer-generated sequences of tones and chords with various amplitudes and durations were delivered to the device through a standard audio amplifier. The resulting droplet motion was captured by using a stationary video post-integrated into the optics of a stereomicroscope. Droplet velocities were later calculated from the video footage by using a frame-analysis algorithm.

Gradient Generation.

The PDMS chip shown in Fig. 6 was secured to the microscope stage and interfaced to the device by using 4-mm i.d. silicone tubing. Gradients were generated by setting cavity output pressures to ≈100 Pa and varying the combination of tones presented to the device. Reservoirs were created by filling a length of tube leading up to the device with dyed water. Both the reservoirs and the discharge line were fixed in level positions at the same height to eliminate hydrostatic driving pressures. The discharge line was fitted with a 1-mm i.d. plastic syringe tip cut to a shallow angle to minimize the pressure buildup associated with drop formation; however, periodic buildup and release of pressure associated with droplet formation at the outlet can still be seen during operation (Movie S3).