Acoustic Levitation For Terahertz Spectroscopy: Optimization, Implementation And Application

Author: Haoye Qin

Mentors: Scott Cushing, Jonathan Michelsen, and William Denman

Editor: Alex Bardon

Introduction

Acoustic waves are capable of trapping particles of a wide range of materials and sizes, compared to the narrower range achieved by optical trapping and magnetic levitation, in which the materials need to be equipped with suitable electromagnetic properties and be dielectric or optically transparent. The special features of acoustic levitation make it a useful tool in container-less transportation, nano-assemblies and the levitation of biological samples or even small animals. Acoustic levitation of liquids can be used to study new fluid dynamics and measure their surface tension or rheological properties.

Conventionally, terahertz spectroscopy for liquid and solid samples suffers from the involvement of either a capillary tube or a glass substrate to hold these samples, which results in unwanted interference from these containers. In this project we employ acoustic levitation to suspend liquid droplet or solid-state materials in the air to obtain their terahertz spectroscopy, thereby avoiding contamination and interaction from the container wall. An acoustic levitator was demonstrated in simulation, optimized for its geometric parameters via a genetic algorithm and implemented for levitation experiments. Liquid droplets and air bubbles were successfully levitated stably, and spectroscopy of target material was achieved. This technique also provides a potential platform for studying air-liquid interface and phase transition and has promising potential applications in extreme ultraviolet (XUV) spectroscopy.

Optimization of acoustic field

An ultrasonic standing wave levitator, also called acoustic levitator, is a device used for levitating fluid and solid particles in an acoustic field. The standing acoustic waves exert an acoustic radiation force on the particles. The force is a second order effect and stems from a combination of the time-averaged pressure and inertial interaction between the particles and the acoustic field.

Finite element simulation of acoustic levitator

To study the distribution of acoustic pressure in an acoustic levitator, an ideal model was set up in COMSOL, a multiphysics simulation software, using its Pressure Acoustics, Frequency Domain (acpr) module. The model was a simplified 2D acoustic levitator geometry driven at a constant frequency, shown in Figure 1.

After the geometry was built up, physical field, boundary condition, specific study and field-probes were properly set in order to conduct the simulation.

**Figure 1.** Two-dimensional geometric model of an acoustic levitator, where Rb is the short axis of the half ellipse, *Length* is height of the rectangle, *Width* is both width of the rectangle and long axis of the half ellipse.

Optimization by Genetic Algorithm

A genetic algorithm (GA) is an algorithm performing randomized search for optimal solutions that draws on the natural selection and natural genetic mechanisms of the biological world. It simulates the phenomenon of reproduction, crossover and gene mutation in natural selection and natural genetic processes. It retains a set of candidate solutions in each iteration and selects better individuals from the solution group according to a specific fitness function. Then it selects these individuals to produce a new generation of candidate solution clusters using genetic operators (selection, mutation, and crossing), repeating this process until some convergence metric is met.

A typical GA flow chart is shown in Figure 2, and a GA was implemented with the parameters in Table 1 to optimize the chosen fitness function: maximum acoustic pressure.

**Figure 2.** Flow chart of a typical GA implementation.

The following table shows the parameters used in this study’s implementation of a GA, which follows typical recommended parameters.

Iterations	Population per Iteration	Mutation rate	Crossover rate	Catastrophic rate
15	20	5%	80%	30%

Table 1. Parameters of the GA.

Livelink between MATLAB and COMSOL

In order to run the GA with data from the objective function, COSMOL was linked to MATLAB as shown in Figure 3.

**Figure 3.** Scheme of implementing GA based optimization for a COMSOL model using MATLAB. Data exchanging routes are shown in this diagram, with the population data in GA being sent into COMSOL for physical simulation and acoustic pressure (Max) data in COMSOL being sent into GA for evaluation of fitness function. This iteration continues until a preset critical condition is met.

Parameter Optimization

The first optimization trial involved leaving only the minor axis of the ellipse (R_b) variable and fixing all other parameters of the acoustic levitator (Length = 75 nm, Width = 55 nm). Since the fitness function, a measure of the system’s success, was designed to be the maximum acoustic pressure in this acoustic levitator, GA optimization results were expected to converge at the highest acoustic pressure. In the second trial, both Width and R_b were set as variables for GA to find the best parameters. For the third trial, all three parameters were set as freely variable.

As shown in Table 2, when all the parameters are set as freely variable, the best acoustic pressure is achieved. This pressure is two orders of magnitude higher than the best pressure that can be achieved with only one variable parameter.

Trial	Width (mm)	Length (mm)	Rb (mm)	Results: Acoustic pressure (Pa)
1	55	75	9.176	3.92×10⁴
2	53.870	75	7.578	2.80×10⁵
3	48.438	69.375	8.672	2.41×10⁶

Table 2. Optimized results of the three trials.

The optimized levitator in 3D perspective

Using the optimized results, simulation models in COMSOL were analyzed, as is shown in Figures 4 and 5.

**Figure 4.** Acoustic pressure distribution in the acoustic levitator with parameters selected by the GA.

**Figure 5.** Acoustic pressure distribution in the so-designed acoustic levitator, shown as a 2D and 1D cross section.

Effect of curvature on the performance of acoustic levitator

As reported by Zurch et al [1] and Michelson et al [2], the acoustic levitation capabilities are strongly dependent on the geometric parameters of the levitator. For reflectors with spherically concave surfaces, a larger section radius results in a greater ability to increase levitation force by choosing an appropriate curvature radius. Michelson et al [2] found that optimal levitation is achieved by applying a reflector with large section radius and small curvature radius with R_b/λ≥0.982. To test the effect of frequency change on the acoustic pressure, we defined the frequency Frequency=k×R_b, where k is a factor for the relationship between R_b and frequency.

Figure 6 demonstrates the relation of parameter k versus the maximum acoustic pressure. The upper panel shows the range from 0.5 to 10 for k, and the bottom panel shows the range from 0.1 to 1.9 for k.

**Figure 6.** Effect of eigenfrequency of the levitator and its acoustic pressure performance.

Here our simulation results showed the maximal value was reached at k=0.1627. By testing frequency dependency in order to gain a better understanding of the effects of the levitator’s operating frequency and geometry on the acoustic pressure, we were able to optimize geometry and available components to maximize acoustic pressure in our levitator. In the future, further error analysis may be conducted based on these results.

Implementation of the acoustic levitation

Samples typically require containers to hold them. For spectroscopy, solid samples usually need glass substrates and liquid samples are taken in nanotubes. These containers introduce contaminants, light reflection and other noises in the spectroscopy results and hinder flexible control of the samples. Acoustic levitation makes it possible to carry out new research because it can hold various substances for experimentation in the absence of containers. It has been applied in the study of spectroscopy, chemical analysis and microgravity organisms. Current levitators are constructed using a Langevin horn and a transducer generating an acoustic wave, which require high tolerances through carefully matched resonant frequencies. This resonance condition is difficult to maintain due to temperature changes caused by conduction heating. In addition, Langevin loudspeakers need to operate at high voltages (>100 V), which can cause problems in challenging experimental environments. Here, we design, build and evaluate a single-axis suspension based on multiple low voltage (about 12 V), well-matched, and commercially available ultrasonic transducers. The suspension operates at 40 kHz in air and captures liquid droplets. The unit consists of low-cost, off-the-shelf components that can be easily assembled using 3D printed sections.

**Figure 7.** Components of the acoustic levitator.

Experimental testing of acoustic levitation

After implementing this device, we experimentally demonstrated the effectiveness of the levitation by levitating liquid droplets and air bubbles stably. In contrast to levitating solid particles in this device, it is trickier to achieve a stable trap for liquid matter. Here a special needle (a straight needle bent to a right angle) was utilized to squeeze a small amount of water around the standing wave in this levitator. Figure 8 demonstrates the performance of levitating one, two and three water droplets in this device, since the distance between the two acoustic-wave-emitting planes allows for several nodes that are suitable for the balance of gravity and acoustic pressure. It is important to note that these levitated states can last for more than several minutes. However, atmosphere disturbance, water evaporation, and unstable power supply can cause failure in stable levitation.

**Figure 8.** Acoustic-levitated water liquid droplets.

For the first demonstration of one droplet levitated, it was measured to be 2.5mm vertically and 4 mm horizontally, as shown in Figure 9(a). This indicates the droplet was stretched horizontally and compressed vertically. This phenomenon can be explained by the fact that in the acoustic field, the liquid droplet is subject to three forces: gravity, surface tension, and acoustic pressure. The combined effects of gravity and acoustic pressure will lead to the compression of the liquid droplet while surface tension will result in its suction. Figure 9(b) illustrates the simulation results of pressure distribution in a small microsphere held in this acoustic levitator.

**Figure 9.** Measuring the size of the acoustic-levitated liquid droplet and simulation explanation for its deformation.

To test the stability of air bubbles, aqueous sodium dodecyl sulfate (SDS) was employed. Figure 10 demonstrates the levitation of three conditions: air bubble embedded in droplet, multi-bubble and single air bubble.

**Figure 10.** Demonstration of the acoustic-levitated air bubbles.

Stable levitation of these bubbles provides a novel platform for studying air-liquid interface and surface tension in liquid droplets. Figure 11 illustrates typical rotating states in these levitated air bubbles, which is due to an initial speed and imbalance in acoustic pressure. We call this phenomenon a “bubble motor” since the rotation of these levitated bubbles is subject to minimal friction and will keep rotating for a long time.

**Figure 11.** Rotation of acoustic-levitated air bubbles.

The shape of the levitated air bubble greatly influences its rotation pattern, and some shapes will not start rotating at all. Therefore, this “bubble motor” could be highly designable and versatile considering a growing body of research in the areas of micro- and nano- motors.

Summary and Future Directions

During this project, optimization, implementation and application of an acoustic levitator have been demonstrated. GA and COMSOL models were employed to optimize the structural parameters of this acoustic levitator for best performance. After implementation, several experiments on liquid droplets, air bubbles and bubble motors were conducted, which indicated the stability and novel capability of the acoustic levitation.

Future work will concentrate on the experimental demonstration of the proposed acoustic-levitated assisted THz spectroscopy. THz spectroscopy employs radiations that lie between the microwave and infrared regions of the electromagnetic spectrum with an approximate frequency range between 0.1 and 10 THz. Terahertz waves are nonionizing, noninvasive, and penetrable to many materials with a depth of penetration lower than that of microwave radiation. Terahertz radiation also tends to be very sensitive to various kinds of resonances such as vibrational, translational, rotational, torsional, and conformational states, enabling it to provide information on molecules that are inaccessible with other analytical and imaging techniques. These unique characteristics make it suitable for identifying, analyzing, or imaging a variety of materials.

Two typical cases are shown in Figure 12, where a liquid sample (i.e. water and aqueous solution) and a solid sample (i.e. 2D materials like graphene and graphene oxide) are under investigation using THz spectroscopy. These two states of materials need to be held with either a thick silica capillary tube or a glass substrate. Drawbacks of using these supporting materials include reflection and contamination to the original THz spectroscopy response.

**Figure 12.** Simplified conventional THz spectroscopy scheme.

Therefore, a solution to these problems is to incorporate acoustic levitation into THz spectroscopy, where the acoustic force serves as a holding technique suitable for both solid samples and liquid droplets. A schematic diagram of these devices is illustrated in Figure 13.

**Figure 13.** The proposed acoustic levitation method for THz spectroscopy.

Due to the wall-less feature of acoustic levitation, the proposed method presents no substrate interaction for solid samples and no tube interaction for liquid samples. In addition, this device provides a platform for studying air-liquid interfaces by employing THz spectroscopy. In summary, acoustic levitation is a technique for spectroscopy with many promising potential applications, and optimization and easy, low-cost implementation of this technique will allow researchers to obtain improved spectroscopy results and perform novel experiments on air-liquid interfaces and phase transitions.

Acknowledgements

I would like to thank Prof. Scott Cushing and all members of the Cushing Group for their guidance and support throughout the duration of this study. I would like to thank the Student Faculties Program at the California Institute of Technology for funding and coordinating my summer research. Finally, I would like to thank the Caltech Library for assistance in 3D printing.

References

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