This document serves as a Design Justification File (DJF) for the Acoustic Levitator Assembly. The main objective of the Acoustic Levitator Assembly is to provide an optimal configuration for accommodating ultrasonic transducers in a way that achieves stable and controlled levitation of a small spherical object. This setup is designed to create a precise acoustic field that can manipulate the position and movement of the object in a controlled airspace without direct contact.
The full report can be found here.
Acoustic levitation operates under two fundamental principles: the Gor'kov potential and the Rayleigh condition.
In acoustic levitation, objects placed within an acoustic field are subjected to forces arising from fluctuations in the surrounding air pressure. These forces are quantitatively described by what's known as the Gor'kov potential. Essentially, the Gor'kov potential is a theoretical construct that provides a mathematical framework for understanding how the pressure variations in the sound waves interact with the physical properties of the object.
This force can be calculated for small, rigid spherical particles using the Gor'kov potential:
Where:
The Rayleigh condition is essential for the validity of the Gor'kov potential. It states that the size of the particles, if considered to be perfectly spherical, needs to be smaller than the acoustic wavelength. Some sources suggest that the particles should be at least twice as small as the wavelength.
For a typical 40 kHz transducer used in acoustic levitation:
Using the formula for wavelength ():
λ = \frac{c}
For 40 kHz:
= = [cm]
The Goal of the Semester Project is to design a prototype of the Payload experiment that will take flight in the Firethorn Rocket in the EuRoC 2025 competition
This year the Payload is to design an acoustic levitation device that is able to maintain a lightweight body in levitation for the longest time possible from liftoff:
The levitation device has two main objectives as defined by the requirements below:
2024_C_SE_PL_ACOUSTIC_LEVITATION_EXPERIMENT_18
Experiment acceleration resistance
The payload experiment shall function when subjected to vertical accelerations of at least [8]g's.
2024_C_SE_PL_ACOUSTIC_LEVITATION_EXPERIMENT_19
Experiment acceleration resistance
The payload experiment shall function when subjected to radial accelerations of at least [3]g's.
EPFL has a lab that is dedicated to research on acoustics (The lab supervising this semester project). Among some of the research they conduct they have a practical where students learn how to use a small scale acoustic levitator and the drawbacks associated to it. The acoustic levitator in their set up is very simple but can give a good indication of the drawbacks and capabilites of such a technology The simulation of the lab acoustic levitator is conducted using Matlab code to predict and analyze the behavior of the levitator under various operational conditions. This simulation is critical for understanding how the device will perform, particularly in terms of the forces exerted on the levitated object [Dolev, 2023].
Creating a bespoke simulation environment for the acoustic levitator involves detailed computation of forces affecting the levitated objects, including the application of the Gor'kov potential. This simulation environment is essential for accurately predicting and optimizing the levitator's performance under various conditions.
Two primary computational methods can be employed to simulate the acoustic levitation phenomena:
Numerical Computation via the Boundary Element Method (BEM): This method is well-suited for problems where the domain is unbounded, such as acoustic fields. BEM focuses on solving linear partial differential equations, specifically Helmholtz equations, which are fundamental in acoustic simulations.
Computational Fluid Dynamics (CFD): CFD can be used to simulate the fluid dynamics around the levitated object, providing insights into how acoustic waves propagate through the medium and interact with objects. This approach is particularly useful for understanding complex interactions in the levitator, such as turbulent flows and the impact of different fluid properties.
Project Scope and Resource Allocation: Developing a dedicated simulation environment is a substantial undertaking that would likely require its own semester project. This project would not only involve software development and simulation setup but also extensive testing and validation against experimental data.
Benefits: Owning a simulation environment allows for tailored adjustments and optimizations specific to our levitator's design and operational needs. It provides a powerful tool for enhancing performance, predicting system behavior under new conditions, and driving innovations in acoustic levitation technology.
Creating this environment would be immensely beneficial, allowing for in-depth studies and refinements specific to our objectives. However, due to the complexity and resources needed, it would necessitate dedicated time and expertise, ideally suited as another semester-long project. All the data we will gather for our acoustic levitator will therefore have to be experimental data.
To systematically test and select the optimal levitator design, we have procured a levitation kit. This kit, developed by the University of Bristol, features simple and cost-effective electronics that can be easily reused for various experimental configurations. Our approach involves the following steps:
Setup the Levitation Kit:
Experiment with Different Levitator Designs:
Select the Optimal Design:
This structured approach ensures a thorough evaluation of potential designs, leveraging the simplicity and versatility of the DIY levitation kit without the need of building a complex simulation environment to test our design.

| Model | Diameter (mm) | Acoustic Output (Pascal/meter*volt) | Phase Standard Deviation (degrees) |
|---|---|---|---|
| Manoshi MSO-P164OH10TR | 16 | 0.25 SD=0.04 | 8.7 |
| MSO-A164OH10T | 16 | 0.36 SD=0.02 | 9.2 |
| MSO-P104OH07T | 10 | 0.13 SD=0.02 | 13.9 |
| Ningbo FBULS1007P-T | 10 | 0.14 SD=0.02 | 13.9 |
| Murata MA40S4S | 10 | 0.17 SD=0.01 | 3.8 |
| MultiComp MCUST10P40B07RO | 16 | 0.25 SD=0.04 | 33.1 |
| MCUSD16A40S12RO | 16 | 0.21 SD=0.03 | 18.3 |
Research by Asier Marzo, Adrian Barnes, Bruce W. Drinkwater, Faculty of Engineering, University of Bristol [Stephens, 2007]
Key Measures:
Explanation:
When selecting the appropriate transducers for our acoustic levitation experiments, two critical factors were taken into account: the acoustic output (pressure generated) and the phase standard deviation.
Acoustic Output: The pressure generated by each transducer at a fixed distance under the same excitation signal was the primary factor measured. This measure is crucial as it determines the ability of the transducer to create a sufficient acoustic pressure field to achieve levitation. Higher acoustic output indicates a stronger ability to manipulate particles.
Phase Standard Deviation: This measure accounts for the variability in the signals produced by the transducers. Even when fed with the same excitation signal, transducers can produce slightly offset signals, which can impact the uniformity of the acoustic pressure field. A lower phase standard deviation is preferable as it indicates more consistent performance and less signal variation among transducers.
| Diameter | Advantages | Disadvantages |
|---|---|---|
| 16 mm | - Better Acoustic Output - Better phase standard deviation |
- Higher Cost - Not ideal given our dimension constraints - Not often used in other acoustic levitators |
| 10 mm | - Lower Cost - Often used in acoustic levitators (including Robotics Practicals) - Smaller (more transducers can be implemented on a smaller surface) |
- Worse phase standard deviation - Worse Acoustic Output |
The decision to utilize 10 mm diameter transducers for our acoustic levitator was driven by several practical considerations:
Cost-Effectiveness: The 10 mm transducers are significantly less expensive, making them a more economical choice for our project, especially when multiple units are required.
Space Efficiency: Their smaller size allows for a denser configuration of transducers within the limited space of our levitator design. This is particularly beneficial in applications where compactness is crucial.
Prevalence in Use: These transducers are commonly used in similar applications, ensuring a reliable performance based on established use cases. Their commonality also implies better availability and community support for troubleshooting and optimization.
Trade-off Acceptance: Although they exhibit worse phase standard deviation and acoustic output compared to 16 mm transducers, these disadvantages are deemed acceptable given the benefits of cost and size. Moreover, these limitations can often be mitigated through careful calibration and system optimization.
By choosing 10 mm transducers, we aim to build a cost-effective, compact, and efficient levitator that meets our specific application needs while staying within budgetary and spatial constraints.
Below is a graph illustrating the trapping force performance of a transducer, depending on the phase standard deviation of the transducers. This graph highlights the superior performance of the Murata MA40S4S, especially notable in its low phase standard deviation which correlates with more stable and efficient trapping force.

Table: Simulation of the trapping force performance of TinyLev (Another type of Transducer) depending on the phase standard deviation of the transducers. by Asier Marzo, Adrian Barnes, Bruce W. Drinkwater, Faculty of Engineering, University of Bristol [Stephens, 2007]
The Murata MA40S4S demonstrates outstanding stability and efficiency in acoustic levitation especially when considering the very strong impact Phase Standard deviation has on such devices, making it the ideal choice for applications requiring precise control and high performance.
This design builds on the Robotics Practicals design by implementing an optimized arrangement of transducers based on the principles of optimal circle packing in a hexagonal pattern. This configuration maximizes the coverage and uniformity of the acoustic field, crucial for enhancing the levitation capabilities of the system. It is inspired by the design of the Acoustic Levitation Kit that was made by the university of Bristol. Here below is a picture of our design [Stephens, 2007].

Hexagonal Packing: The transducers are arranged in a hexagonal pattern, which is known for its efficiency in space utilization and coverage. This pattern is especially beneficial in applications like acoustic levitation where uniform distribution of acoustic pressure is necessary.
Detailed Transducer Arrangement:

Initial Setup: The initial configuration includes 7 transducers — one at the center and six surrounding it in a ring. This setup forms the basic module of the hexagonal packing pattern.
Scalability: While the basic setup includes 7 transducers, the design allows for easy scaling by adding more transducers following the same hexagonal pattern. This scalability makes the design versatile for different sizes and shapes of the levitated objects.
In the development of our acoustic levitator, we consider several focusing strategies that significantly influence the trapping force capabilities of the system. Each strategy comes with its own set of trade-offs in terms of complexity, cost, and performance:
(a) Flat Surface Transducers: This strategy employs a straightforward construction method, using flat surface transducers that are easier and cheaper to produce and assemble. However, the main drawback is the relatively low trapping force they generate, which may not be sufficient for applications requiring the manipulation of heavier or more resilient materials.
(b) Electronic Phase Adjustment: By dynamically adjusting the phase of the acoustic waves through electronic control, this method can significantly enhance the trapping force. The electronic phase adjustment allows for precise control over the acoustic field, enabling better manipulation of the levitated objects. However, this method requires advanced, complex electronics which increase the system's cost and complexity, potentially making it less accessible for smaller-scale or budget-constrained projects.
(c) Fixed Physical Phase-Delays: As an alternative to electronic controls, fixed physical phase-delays can be implemented. This method involves structurally designing the transducer setup to create phase delays, which manipulate the acoustic field similarly to electronic adjustments. This strategy offers a performance comparable to electronic phase adjustment but with potentially reduced complexity and cost since it does not rely on sophisticated electronic systems.
The graph below, taken from a study by the University of Bristol, illustrates the trapping forces achieved with different trapping strategies. It plots the trapping force relative to each strategy, providing a visual representation of how each method impacts the overall performance of the levitator.

(d) The vertical transducer movement and orientation strategy has been identified as the most effective method for achieving optimal trapping capabilities. This approach involves adjusting the vertical position and angle of the transducers to align precisely with the levitated object, thereby maximizing the acoustic force exerted directly where it is most effective.
Focused Acoustic Energy: By orienting the transducers vertically, the acoustic waves are directed more efficiently towards the levitation point. This concentration of energy results in a stronger and more stable levitation force, capable of handling objects with greater precision and control.
Enhanced Stability: Vertical alignment helps maintain the object at the nodal point of the acoustic field, where the opposing forces balance perfectly. This stabilization is crucial for applications requiring high precision and minimal disturbance.
Adaptability: Vertical movement allows for quick and easy adjustments to the system, accommodating different sizes and shapes of objects without extensive reconfiguration of the entire setup.
Main Problem: Size
Solution:
| Aspect | Advantages | Disadvantages |
|---|---|---|
| Design Flexibility | - Flexible design (can easily re-print, add extra transducers, change the distance between the two domes) | - Complicated electronics because of the motor |
| Cost Efficiency | - Requires few transducers (Low cost of the levitation device) | - Motor significantly increases the cost |
| Performance | - Improved radial performance thanks to the motor | - Hard to test |
Despite the benefits outlined, we ultimately decided not to proceed with Design I. While the design presents a flexible and potentially cost-effective solution, we believe that there is still room to find a more optimal configuration that better meets our needs. Additionally, the integration of the motor significantly complicates the testing process, presenting challenges that might hinder efficient development and evaluation. Furthermore, we were quite sure that this design would not be able to hold the 8g accelerations required for our application. These factors led us to continue exploring other design possibilities that may offer improved ease of testing and overall performance without the complexities introduced by the motor system.
This design integrates a 3-axis transducer arrangement to effectively compensate for radial acceleration forces. The three-axis control allows for precise manipulation of the acoustic field, enhancing stability and control during levitation and is especially effective when it comes to stabilizing a particle under radial accelerations. This design is inspired by various reasearch in the field that have testing similar configurations but at different scales and different applications [Marzo, 2022].

3-Axis Transducer: Each transducer phase can be adjusted, allowing for precise control over the acoustic forces applied to the levitated objects.
Dome Setup: The system comprises 6 domes, each outfitted with 7 transducers, totaling 42 transducers. This setup is designed to ensure a comprehensive and uniform acoustic field.
Motor Replacement: This design eliminates the need for motors by having a 3-axis device and having more stability against radial accelerations, which simplifies the mechanical design and reduces maintenance.
| Aspect | Advantages | Disadvantages |
|---|---|---|
| Testing and Maintenance | Simpler to test due to reduced mechanical complexity | High cost due to the large number of transducers |
| Stability and Performance | Enhances particle stabilization against radial accelerations | Requires significant space |
| Manufacturing and Design | Reduces the need for complex motor systems | Challenges in manufacturing and potential vibration sensitivity |
While this 3-axis transducer design marks an improvement over previous setups by offering more direct control over levitation forces, there is potential for further optimization. The current design, while effective, still occupies a considerable amount of space and incurs high costs due to the extensive use of transducers. These factors are significant when considering scalability and practical application. We anticipate that these insights will guide the development of Design III, where we aim to address these inefficiencies and refine the system to achieve better optimization and practicality.
Design III simplifies the overall transducer setup by reducing the number of transducers to 19 per dome, arranged in an optimal configuration that balances lateral and longitudinal force exertion. This design results from continued optimization efforts, focusing on achieving the best trade-off between controlling vertical and radial forces.


| Aspect | Advantages | Disadvantages |
|---|---|---|
| Compactness and Efficiency | Very compact and spatially optimal | Will need rigorous testing as such designs haven’t been used often |
| Cost-effectiveness | The cheapest design among the considered alternatives | |
| Force Balance | Excellent trade-off in stabilizing the particle against vertical and radial forces |
Design III was selected as the preferred configuration due to its effective balance of transducer economy and performance. It significantly improves upon previous designs by reducing complexity and cost while maintaining high functionality. The chosen setup allows for a compact design, minimizing the space required and simplifying the assembly process. The 8.5 mm gap specifically accommodates the camera system, ensuring unobstructed monitoring of the levitation process. This design will be the basis for further refinement and testing to ensure its feasibility in practical applications.
Shape and Configuration: The design featured a perfect spherical shape with a small aperture to allow camera visibility inside the levitator. This configuration provided optimal trapping forces due to the symmetry and uniformity of the acoustic field.
Material: The sphere was initially 3D printed using regular PETG. While PETG offered sufficient structural resistance for the levitation forces, its high melting point posed challenges during manufacturing.
Challenges:

Shape and Configuration: To enhance usability and manufacturing stability, the design was modified to include an 8.5 mm gap between two half-spheres. This gap facilitated camera visibility and also significantly improved access for manipulating the internal components.
Material: The second iteration utilized High-Temperature PETG (HTPETG), which retains the structural advantages of regular PETG but with greater resistance to high temperatures.
Advantages:
By addressing the practical and manufacturing challenges encountered in the first iteration, the second iteration of Design III allowed for better usability and durability of the levitation device, making it more suited for experimental applications.

Stephens, 2007
Three-axis acoustic device for levitation of droplets in an open gas stream and its application to examine sulfur dioxide absorption by water droplets
Terrance L Stephens, Ralph S Budwig
PMID: 17503939
DOI: 10.1063/1.2424454
Marzo, 2022
TinyLev: A multi-emitter single-axis acoustic levitator
Asier Marzo, Adrian Barnes, Bruce W. Drinkwater
© 2022 IEEE
IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control (Early Access)
Röthlisberger, 2022
Multi-Frequency Acoustic Levitation and Trapping of Particles in all Degrees of Freedom
M. Röthlisberger, G. Schmidli, M. Schuck, J. W. Kolar
ETH Pioneer Fellow Marcel Schuck is developing a robotic gripper that can manipulate small and fragile objects without touching them. The technology is based on sound waves.
Dolev, 2023
Acoustic Levitation apparatus (Robotics Practicals)
Dolev, Amit; Noseda, Lorenzo Francesco John; Yalcin, Bora; Sakar, Selman