Over the years, a diverse range of physical and chemical phenomena have been explored and applied to devise reliable, small thrusters for stationkeeping and orientation of spacecraft. Commercial space flight is accelerating this need. Here, we consider acoustically driven melting of a frozen working fluid in the nozzle of an acoustic device, followed by acoustofluidic atomization from the nozzle to produce thrust. Fifty-five MHz acoustic waves generated by piezoelectric transducers couple into liquid and transfer energy in the form of both acoustic radiation and streaming, producing a directed atomized spray. A challenge in this system, as with most liquid-thrust systems, is the risk of phase change due to the extreme thermal environment in space, particularly in the freezing of the working fluid. Though acoustic energy is known to produce rapid and controllable heating, it so far has not been used to produce phase changes. The atomization produces capillary pressure sufficient to draw in fluid from a reservoir, though we do use a simple pressure-driven pump to support greater atomization rates. We provide a simple energy conservation model to explain the acoustothermal interaction and validate this with experiments. The specific impulse and thrust of this type of thruster are quite modest at 0.1–0.4 s and 12.3 μN, respectively, but the thruster component is small, light, and is without moving parts, a fascinating potential alternative to current technologies.
With thousands of launches per year required for advanced telecommunications applications,1 alongside interplanetary missions for tiny “Cubesat” satellites2 and tourism flights into low earth orbit,3 there has never been so many space-bound platforms in need of small thrusters,4 which can reliably produce micro- to milli-Newtons of thrust while accommodating restrictive mass, volume, and power constraints. Many physical and chemical phenomena have been considered, including chemical thrusters,5 cold gas thrusters,6 Hall effect and ion thrusters,7 and electrospray thrusters.8 A new technology, film-evaporated microelectromechanical systems tunable array (FEMTA), offers good efficiency and is compact and low mass but offers relatively low absolute thrust and specific impulse.9 Generally, the mass of these systems tailored to small satellites is not widely reported, though a general idea can be gathered from Miller et al.,4 where the total mass of the system absent the working fluid is around 1 kg and the thruster itself is around 0.1 kg. Cold gas thrusters generally offer thrust values at 1 mN order and a specific impulse of around 50 s. Chemical thrusters offer a specific impulse of 50–500 s and 1–10 N thrust. Electric thrusters offer superior specific impulse on the order of 1000 s but relatively small thrust values of 0.1–10 mN.
We propose a different approach using acoustic heating to produce a solid–fluid phase change that leads to acoustic atomization. The vision here is the elimination of valves and other complexities by using a working fluid that can be allowed to freeze in the nozzle of an acoustofluidic thruster, thus rendering the thruster inert until needed. Small liquid volumes are known to increase in temperature when they are exposed to acoustic waves upon a substrate,10 even to the extent that it has been used to enhance chemical reactions.11–13 Wang et al. concluded that heat was generated within the liquid itself, not at the interface.14 Huang et al. examined acoustically driven atomization and discovered that heat transfer is important in the process.15 High frequency surface acoustic wave (fSAW) and thickness-mode transducers eject droplets from a fluid in contact with the surface of the transducer with a velocity of ∼1 m/s.10,16–18 It is, furthermore, possible to continuously and linearly control the direction of droplets ejected from the source19,20 to over 50° off-axis, suggesting the potential of a steerable thruster with no moving parts. The overarching phenomenon—acoustofluidics21,22—is used in various other applications but here can be used to generate thrust dependent on the flow rate and velocity of the ejected droplets. Piezoelectric transducers used in this work are low in mass and volume and miniaturized driving electronics have already been developed.23
Here, we specifically consider a focused 55.5 MHz SAW (fSAW) device constructed24 on 127.68° Y-rotated lithium niobate (LN) capable of producing thrust via atomization of water fed to it through a 100 μm nozzle. We choose LN as it exhibits no hysteresis,16 unlike polycrystalline piezoelectric alternatives that offer less tolerance to temperature extremes and produce greater energy losses.25
We first sought to determine the extent to which SAW generated by our acoustic device would be able to melt a 1.00 ± 0.01 frozen drop of de-ionized (DI) water sitting upon the LN (Fig. 1) at the focal spot of the fSAW structure. The LN substrate was in a direct physical contact with a Peltier thermoelectric control module (TEC, TECF2S, Thorlabs, ΔT C, Imax = 1.9 A) as shown in Fig. 1. The experiment was conducted in a lab maintained at C.26 Driven with a power supply (DC Power Supply, YH-305D, YiHUA), the TEC was mounted upon a heat sink (ATS-54425D-C1-R0, Advanced Thermal Solutions) that was in turn placed in an ice water bath so that the “hot” side of the TEC was maintained at C through all experiments.
A 55.5 MHz fSAW LN transducer was placed upon an 18-mm square thermoelectric cell (TEC) for our experiment. A 1.00 ± 0.01 (1.00 ± 0.01 mm3) sessile drop of de-ionized water was then placed at the focal spot of the fSAW. The bottom of the TEC was immersed in a water ice bath to facilitate freezing of the water droplet on the fSAW surface. For clarity, the objects in the figure are not to scale.
A 55.5 MHz fSAW LN transducer was placed upon an 18-mm square thermoelectric cell (TEC) for our experiment. A 1.00 ± 0.01 (1.00 ± 0.01 mm3) sessile drop of de-ionized water was then placed at the focal spot of the fSAW. The bottom of the TEC was immersed in a water ice bath to facilitate freezing of the water droplet on the fSAW surface. For clarity, the objects in the figure are not to scale.
The fSAW device surface temperature was measured via thermocouple (TJ1-CAIN-IM15G-600 and HH911T, Omega Engineering, Inc., Norwalk, CT, USA) while the sessile drop temperature was measured via an infrared (IR) camera (FLIR A35 FOV 13, Teledyne FLIR LLC, Wilsonville, OR, USA), calibrated with the thermocouple. The fSAW device was driven with a signal generator (WF1967 multifunction generator, NF Corporation, Yokohama, Japan) and amplifier (5U1000, Amplifier Research Corp., Souderton, Pennsylvania, USA) and measured using an oscilloscope (InfiniiVision 2000 X-Series, Keysight Technologies, Santa Rosa, CA, USA) with voltage and current probes. The vibration displacement and velocity of the surface of the fSAW device were measured by a laser Doppler vibrometer (LDV, UHF-120, Polytec, Waldbronn, Germany). The 1 DI water droplet was dyed with 0.005 ± 10−4 g of sulforhodamine B (MilliporeSigma, St. Louis, MO, USA) only for the images presented in this Letter. In any case, it did not alter the water's freezing or thermodynamic characteristics, verified with non-dyed de-ionized water that was used for data collection. We next pipetted a sessile drop of 1 ± 0.1 DI water at the fSAW focal spot and froze it at several different temperatures below 0 °C. The temperatures were selected by adjusting the current input into the TEC.
After establishing these initial states, we applied a signal into the focused interdigital transducer (fIDT) to determine how easily the droplet could be melted, a process illustrated in Fig. 2. During these experiments, we collected video of the system as provided in Fig. 3. Each experiment was repeated three times to ensure the robustness of our observations. Water condenses and freezes across the fSAW device substrate when the surface temperature is reduced below 0 °C in the laboratory. If the fIDT itself were producing significant heat via resistive heating, then we would expect isotropic melting outward from the fIDT. The thin ice layer instead melts specifically where SAW is propagating. Resistive heating in the fIDT appears to be negligible in comparison to the effect of the SAW. We also compared the temperature of the LN substrate outside the SAW path to the droplet temperature in Fig. 4, referring to the two dashed circles in Fig. 2(b). As the power into the fSAW is increased, the droplet's temperature increases above freezing for most combinations of the fSAW input power and starting equilibrium temperature. The TEC setting of C produces a similar temperature for the substrate and droplet, as the TEC is unable to draw heat from the fSAW device at a rate sufficient to maintain the C for the substrate as the droplet is heated. At lower TEC equilibrium temperatures, however [see Figs. 4(b)–4(d)], its ability to draw heat from the droplet and substrate is increased. In these conditions, the droplet's temperature during the application of fSAW remains greater than the adjacent substrate, indicating that the droplet is the source of heating when exposed to acoustic energy. We next considered the frozen sessile drop as a thermodynamic system in equilibrium below freezing, as set by the TEC. Heat influx from the laboratory environment is balanced with heat flux removed by the TEC. Now consider a new source of energy turned on at time t = 0, in this case, a voltage signal is applied to the fIDT to cause acoustic energy to propagate into the drop. We assume some fraction, α, of the input power, , to the fIDT generates heat in the frozen sessile drop. Water ice is known to have an acoustic loss mechanism that generates heat, but this mechanism is usually considered in the entirely different contexts of acoustic wave propagation in ice floes27,28 and aircraft icing.29 The frozen sessile drop will also radiate heat to the laboratory environment and conduct heat to the substrate. Therefore, the energy balance is
as governed by the first law of thermodynamics, where is the heat transfer into the system, and are heat fluxes due to radiation and conduction, is the input power to the fIDT, and α is the effective loss coefficient from input power to heat energy output into the droplet. Impedance mismatches and acoustic energy either lost at the reflectors or bypassing the fluid collectively contribute to a value of α of less than one. Integrating Eq. (1) from t = 0 to the time when the drop has fully melted produces the total energy change required to melt the sessile drop on the left-hand side, consisting of the heat capacity of ice, , and the latent heat of phase transformation, . On the right-hand side, the energy contributions from radiation, conduction, and acoustic energy input via the fIDT appear as , and , respectively. Presuming is constant over and dividing both sides by the energy terms produces the following expression for the time required to melt the drop:
where c is the heat capacity of ice, m is the mass of the drop, k is the droplet's thermal conductivity, is the difference in temperature between the droplet and the environment, is the difference between 0 °C and the initial temperature set by the TEC, is the latent heat of transformation from ice to liquid water, is the change in time, ϵ is the emissivity of ice, σ is the Stefan–Boltzmann constant, is the surface area between the drop and the environment, and is the surface area between the drop on the substrate.
A 1 frozen DI water droplet was melted by internal acoustic losses. The fIDT can be seen at the top and the sessile drop at the center of each frame. (a) An LDV scan shows the relatively narrow region over which fSAW exists during activation, about one-third of the aperture width and progressively more narrow over the measured region. The sessile water droplet was placed at the pink circle marked in this image. (b) Initially, the droplet was frozen through the action of the TEC and maintained at −13.63 ± 0.05 °C. Note the frost appearing across the surface of the device due to condensation. The temperatures were measured at the regions denoted with dotted circles. (c) Applying 1.10 ± 0.05 W at 55.5 MHz to the fIDT starts melting the water after 2.4 s. Note that the frost remains outside of the fIDT aperture but melts inside the aperture. (d) After 4.8 s, the frozen droplet is partially melted, principally in the viscous boundary layer in contact with the SAW substrate. (e) The fSAW completely melts the drop after ∼7.2 s. Scale bar is 2 mm (see Fig. 3).
A 1 frozen DI water droplet was melted by internal acoustic losses. The fIDT can be seen at the top and the sessile drop at the center of each frame. (a) An LDV scan shows the relatively narrow region over which fSAW exists during activation, about one-third of the aperture width and progressively more narrow over the measured region. The sessile water droplet was placed at the pink circle marked in this image. (b) Initially, the droplet was frozen through the action of the TEC and maintained at −13.63 ± 0.05 °C. Note the frost appearing across the surface of the device due to condensation. The temperatures were measured at the regions denoted with dotted circles. (c) Applying 1.10 ± 0.05 W at 55.5 MHz to the fIDT starts melting the water after 2.4 s. Note that the frost remains outside of the fIDT aperture but melts inside the aperture. (d) After 4.8 s, the frozen droplet is partially melted, principally in the viscous boundary layer in contact with the SAW substrate. (e) The fSAW completely melts the drop after ∼7.2 s. Scale bar is 2 mm (see Fig. 3).
Video: Acoustically driven melting of a frozen sessile (water) droplet via viscous losses in the frozen media. Multimedia view: https://doi.org/10.1063/5.0131467.1
Video: Acoustically driven melting of a frozen sessile (water) droplet via viscous losses in the frozen media. Multimedia view: https://doi.org/10.1063/5.0131467.1
The measured temperatures of a spot on the substrate (in orange) and of the drop (in blue), where each location is indicated in Fig. 2(b). Each plot represents data taken at a single TEC setting: (a) TEC set to , (b) TEC set to , (c) TEC set to , and (d) TEC set to .
The measured temperatures of a spot on the substrate (in orange) and of the drop (in blue), where each location is indicated in Fig. 2(b). Each plot represents data taken at a single TEC setting: (a) TEC set to , (b) TEC set to , (c) TEC set to , and (d) TEC set to .
Once the melting interface propagates to the sessile drop, it fully melts the drop in a few seconds, as plotted in Fig. 5 in comparison with the melting time predicted from Eq. (2). Our fSAW devices had one or two 14-finger-pair fIDTs; at 55.5 MHz, the electromechanical coupling may be calculated30 for these devices to be approximately 15%, implying 15% of the energy passed electrically to the device became a SAW propagating across the substrate. This also implies that 85% of the input power is electrically reflected—not lost, but unavailable to use in generating acoustic waves in the SAW device. Assuming that one-half of the acoustic power generated by the fIDT is subsequently lost at the reflector (see Fig. 6), then 7.5% of the input power is actually made available to produce heating of the droplet. The result of this model roughly matches the data. We also include an additional term proportional to the TEC current, , where I is the current in the TEC, necessary to properly account for the different equilibrium temperatures, because the thermodynamics of the TEC is surprisingly complex:31 not only does it set the temperature but it also extracts heat from our system at a rate weakly dependent upon its input current. Finally, we eliminate the radiation heat transfer term as its contribution is negligible in our system: the temperature of the environment had little observable effect on the melting of the droplet. Our modified model is given as follows:
which agrees quite well with the data with these two mechanism-based fitting parameters. We may conclude that our model represents the major thermal mechanisms present in our experiments.
The time required to melt a 1 frozen droplet of water, starting from the indicated equilibrium temperatures. Experimental data are provided as discrete points; our model is plotted as continuous lines in the corresponding color. Notice that no experimental dots appear in yellow, green, or red below the power at which the corresponding model line becomes asymptotic. Drops actuated at these low powers did not melt when the TEC was set below C. The time to melt was consistently 10 s or less regardless of the initial temperature when using 1 W or more for the fSAW (see Fig. 3).
The time required to melt a 1 frozen droplet of water, starting from the indicated equilibrium temperatures. Experimental data are provided as discrete points; our model is plotted as continuous lines in the corresponding color. Notice that no experimental dots appear in yellow, green, or red below the power at which the corresponding model line becomes asymptotic. Drops actuated at these low powers did not melt when the TEC was set below C. The time to melt was consistently 10 s or less regardless of the initial temperature when using 1 W or more for the fSAW (see Fig. 3).
A paired fSAW design as a thruster, with a small, 100 μm, through-hole laser cut in the substrate. Water was supplied via a syringe pump at a given mass flow rate matching the atomization rate. The fIDT and reflector pattern, the fluid meniscus, and the atomized droplets are not to scale for clarity.
A paired fSAW design as a thruster, with a small, 100 μm, through-hole laser cut in the substrate. Water was supplied via a syringe pump at a given mass flow rate matching the atomization rate. The fIDT and reflector pattern, the fluid meniscus, and the atomized droplets are not to scale for clarity.
At the lowest input power, there was insufficient energy to melt the drop except for the highest initial temperature set by the TEC. This agrees with our model since the melt time trends to infinity as the fSAW input power is reduced below about 0.5 W in our system (see Fig. 5). In cases where the drop did eventually melt, the melting time was greater for lower initial temperatures and lower fSAW input power. However, at high fSAW powers beyond about 1 W, there was little difference between the melt time for any of the four starting temperatures. This likely indicates that conduction and radiation, which depend on the temperature difference between the droplet and its surroundings, play a larger role when the fSAW power is lower. At high fSAW power, there is less time for this temperature difference to have an effect through conduction and radiation. Instead, the energy introduced by the fSAW device is overwhelming. Moreover, as the reader may suspect, the energy required to produce the phase change—the latent heat—is the dominant component in this system.
An fSAW device nearly identical to the one used for melting frozen water samples in the previous experiment was used to create a prototype thruster (Fig. 6). There were two key differences: a pair of fSAW IDTs were used instead of just one, both focused at a central point, and a rudimentary nozzle, a 100 μm, capillary through-hole, was laser machined into the substrate at this location using a 1030-nm femtosecond pulsed laser at 9 mJ cm−2 and 60 kHz pulse rate (LightShot, Optec Laser, Frameries, Belgium). A small silicone tube was attached to the underside of the substrate via a barb nipple glued to the substrate using ultraviolet-cured epoxy (NOA61, Norland Products, Jamesburg, NJ, USA). The other end of the tube was connected to a DI water-filled 50 ml syringe placed in a syringe pump to supply the working fluid at a rate matching the atomization rate. Larger flow rates cause leaking of non-atomized fuel and smaller flow rates needlessly reduce the thrust to power ratio. This fluid supply mechanism will be replaced in future prototypes in favor of a wicking mechanism32,33 suited to zero gravity.
Drive signals were then supplied to both fIDTs on the device. When the fSAW power from each side is equal, water is atomized directly upward at a velocity dependent on the total power as shown in Fig. 7. When fSAW power from one side is greater than the other, the direction of atomization changes, producing angled atomization as shown in Fig. 8. The atomization was imaged from the side at 6400 fps to calculate the exit velocity of the atomized droplets for different fSAW power inputs as provided in Table I. The flow rate was used with the droplet ejection velocity to calculate the equivalent thrust, . Here, ve is the exit velocity of the working fluid and Qf is the mass flow rate. It is worth noting here that the direction of each atomized droplet's ejection from the parent droplet is along the net acoustic wave propagation direction in the parent droplet, and so the estimate of the thrust generated in this system with our approximate approach is reasonable. The surface tension surrounding each forthcoming atomized droplet is approximately the same: the parent droplet is much larger, leaving curvature of the parent droplet less of an issue than when ejecting large jets and droplets.19 The subsequent spread of the droplets occurs due to drag with the surrounding quiescent air. This is different than when ejecting droplets from an orifice, where drag by the orifice changes the direction of the ejected droplets during ejection to cause some to have significant momentum oriented away from the axis of the main atomization.
Video: Acoustically driven ejection of sessile droplets of working fluid. Multimedia view: https://doi.org/10.1063/5.0131467.2
Video: Acoustically driven ejection of sessile droplets of working fluid. Multimedia view: https://doi.org/10.1063/5.0131467.2
Video: Acoustically driven continuous atomization and steering of working fluid. Multimedia view: https://doi.org/10.1063/5.0131467.3
Video: Acoustically driven continuous atomization and steering of working fluid. Multimedia view: https://doi.org/10.1063/5.0131467.3
Focused SAW is supplied from both IDTs and impinges on a liquid supplied at a chosen mass flow rate. The power indicated is the sum of the power from two IDTs.
Input power (W) . | Flow rate (ml/min) . | Exit velocity (m/s) . | Thrust (μN) . | Specific impulse (s) . |
---|---|---|---|---|
1.00 | 0.025 | 1.7 | 0.706 | 0.173 |
2.00 | 0.1 | 2.8 | 4.65 | 0.286 |
3.00 | 0.2 | 3.7 | 12.3 | 0.378 |
Input power (W) . | Flow rate (ml/min) . | Exit velocity (m/s) . | Thrust (μN) . | Specific impulse (s) . |
---|---|---|---|---|
1.00 | 0.025 | 1.7 | 0.706 | 0.173 |
2.00 | 0.1 | 2.8 | 4.65 | 0.286 |
3.00 | 0.2 | 3.7 | 12.3 | 0.378 |
A potential problem is the effect of allowing water to freeze and expand in the machined hole of the fSAW device. The water's expansion could cause failure of the material. We froze two different devices laden with water over ten times and found no failure, cracks, or other flaws during subsequent operation. During the use, the hole in the LN substrate is subjected to substantial tensile and compressive stresses at 55.5 MHz; flaws either already present or introduced during freezing would likely lead to failure of the device.
The device demonstrated here produces melting and atomization of a 1 drop with an input power on the order of 1 W and is capable of producing thrust in the range 1–10 μN, which is substantially less than the 1 mN to 10 N thrusters available using other methods. Moreover, the specific impulse is 0.1–0.4 s, two orders of magnitude less than cold gas thrusters that produce 50 s, and three orders of magnitude less than electric thrusters. However, the approach is interesting considering the thruster itself is mm3 in size, 0.6 g mass, and potentially scalable. The electronics are approximately 5–10 g today;23 ASIC (application-specific integrated circuit) options may reduce the driver mass34 to 0.5 g. This excludes the mass of the working fluid, piping, and other necessary components that are important to consider in a full application design. A major advantage of this method is that by simply adjusting the drive signals input into the fIDTs, the direction and amplitude of thrust can be finely tuned with no moving parts.
The work presented here was generously supported by a research grant from the W. M. Keck Foundation and by the Office of Naval Research (via Grant Nos. 12368098 and 13423461) to J. Friend. The authors are grateful to the University of California and the NANO3 facility at UC San Diego for provision of funds and facilities in support of this work. This work was performed in part at the San Diego Nanotechnology Infrastructure (SDNI) of UCSD, a member of the National Nanotechnology Coordinated Infrastructure, which was supported by the National Science Foundation (Grant No. ECCS-1542148). The authors are also grateful to John Roy and team in San Diego from Optec Laser Systems, for substantial training, assistance, and advice throughout this effort.
AUTHOR DECLARATIONS
Conflict of Interest
The authors have no conflicts to disclose.
Author Contributions
Amihai Horesh: Investigation (equal); Methodology (equal); Writing – original draft (equal). William Connacher: Formal analysis (equal); Investigation (equal); Methodology (equal); Resources (equal); Visualization (lead); Writing – original draft (lead). James Friend: Conceptualization (lead); Formal analysis (lead); Funding acquisition (lead); Investigation (lead); Project administration (lead); Resources (lead); Supervision (lead); Writing – review & editing (lead).
DATA AVAILABILITY
The data that support the findings of this study are available from the corresponding author upon reasonable request.