Acoustic Levitation and Trapping

Acoustic levitation allows objects to be suspended in air or in liquids without falling. In this episode, we speak with Philip Marston (Washington State University) about the history of acoustic levitation, and his work to translate previous research into terminology more accessible to modern readers and those outside of the field of physics.

Associated papers:
- Philip L. Marston. "Trapping in acoustic standing waves: Effect of liquid drop compressibility." J. Acoust. Soc. Am. 154, R5–R6 (2023). https://doi.org/10.1121/10.0020809

- Philip L. Marston. "Contrast factor for standing-wave radiation forces on spheres: Series expansion in powers of sphere radius." JASA Express Lett. 4, 074001 (2024). https://doi.org/10.1121/10.0027928.

- Philip L. Marston. "Position dependence of the standing-wave radiation pressure quadrupole projection on a sphere applied to drop shape." J. Acoust. Soc. Am. 156, 1586–1593 (2024). https://doi.org/10.1121/10.0028518.

Read more from The Journal of the Acoustical Society of America (JASA).
Read more from JASA Express Letters.
Learn more about Acoustical Society of America Publications.

Music Credit: Min 2019 by minwbu from Pixabay. 

Transcript

Kat Setzer  00:06

Welcome to Across Acoustics, the official podcast of the Acoustical Society of America's publications office. On this podcast, we will highlight research from our four publications. I'm your host, Kat Setzer, Editorial Associate for the ASA.

Kat Setzer  00:25

Today I'm talking to one of the ASA's long-time members and an influential thinker in the field of physical acoustics, Dr. Philip Marston. Typically, we discussed one article, but when we started talking about most of his most recent JASA paper, "Position dependence of the standing wave radiation pressure quadrupole projection on a sphere applied to a drop shape," we realized that it would be important to go back into the history of this work a bit further, so we're going to talk a bit about some of his past articles as well, to hopefully give our listeners a better understanding of acoustic levitation. With all that said, thank you for taking the time to speak with me today, Phil, how are you?

Philip Marston  00:59

Oh, thank you. This is, I think, a good opportunity to try to help the community. 

Kat Setzer  01:04

Yeah, I feel like I'm going to learn a lot. So first, tell us a bit about your research background. 

Philip Marston  01:08

Well, I became interested in measuring in acoustical spectra while I was in high school in the 1960s and I would actually go down to the Seattle Public Library to read the Journal of the Acoustical Society of America back then. Then by graduate school, my interests included optical and acoustical scattering and radiation pressure on bubbles. Providentially for me, Bob Apfel in the late 1970s gave me a chance to work as a postdoc with him on radiation pressure and levitation, and that was prior to my coming to Washington State University. 

Kat Setzer  01:42

Okay, okay. So what do you mean when you discuss trapping a particle in an acoustic standing wave? And why is it important? 

Philip Marston  01:50

Well, the basic idea is to use the time average forces of acoustic waves to manipulate objects such as particles, drops or bubbles. And more recently, people are doing this with biological cells. One of the goals is to measure properties without touching an object. In some cases, the objects of interest become unstable if touched. In addition, acoustical manipulation could include spinning or rotating objects.

Kat Setzer  02:20

Okay, okay, so I've heard people talk about acoustic levitation. Is this concept related? And if so, how?

Philip Marston  02:27

Acoustic levitation allows objects to be suspended in air or in liquids without falling. The phrase was generalized to include holding down air bubbles or oil drops in water that would float upward, levitation, again uses time average forces of acoustic waves. 

Kat Setzer  02:49

So when you were preparing for this interview, you mentioned that your two recent articles from July 2024 and September 2024 really were created to explain previous research for modern readers. Can you give us some background on the history of the study of trapping particles in acoustic waves. 

Philip Marston  03:05

Well, in a JASA Reflections article in September 2023, I recalled related experiments on trapping drops and bubbles from the late 1960s and early 1970s. The emphasis was on a key experimental paper by Larry Crum to very verify the predicted dependence on the compressibility of oil-like drops acoustically trapped in water. I also discussed in that Reflection article the impact of that investigation on measuring properties of levitated drops, including, for example, optical scattering properties.

Kat Setzer  03:50

Okay, okay, so what is the radiation force on spheres in standing waves, and why would you want to know this force? 

Philip Marston  03:57

This is the time average force that enables the sphere to be trapped. knowing the force tells you the amplitude of the ultrasonic wave needed to achieve a given objective.

Kat Setzer  04:10

Okay, got it. That's very simple. So what is the acoustic contrast factor and how is it typically used?

Philip Marston  04:16

By 2005 some researchers, to simplify the discussion of the forces, grouped together as a contrast factor the compressibility and density parameters, relevant to Larry Crum's 1971 experiment. So again, the compressibility factor tells you the change of volume of object when you pressurize it, or when the acoustic wave pressurizes it. And the density parameters tell you the contrast between the density of the object that you're trying to trap or manipulate and that of the surrounding medium. So these are going to be quite different for the case of, say, oil-like drops levitated or trapped in water or biological cells, or the case of liquid drops trapped in air. 

Kat Setzer  05:08

Okay, okay. Got it. So in your JASA Express Letters article, which was published in July 2024, you aimed to translate your past research into terms of the acoustic contrast factor. Why did you want to do this?

Philip Marston  05:22

I realized that it could help some researchers to comment on the relationship of different ways of expressing acoustic radiation forces. For example, after the appearance in the late 1970s in JASA, some of the experiments and analysis of radiation forces use a dimensionless radiation force function. The dimensionless radiation force function was introduced in a series of papers published by researchers in Japan, many of them published in the Journal of the Acoustical Society, that was used to describe how the radiation forces depended not only on the properties of objects, but also their size and some aspects of the acoustic wave field. 

Kat Setzer  06:15

Okay.

Philip Marston  06:16

They were often used to express the relationship with size-dependent scattering properties. With students, I had used dimensionless radiation force functions in various JASA papers between 2006 and 2022, so I thought it would be helpful to expand on the relationship with the contrast factor when appropriate. 

Philip Marston  06:41

So concerning the most recent two articles, the July Express Letters article really had the objective that you can calculate radiation forces on simple spherical objects in a standing wave in a way that reveals how this depends on size, how these forces depend on size. And it's not actually limited to the case of liquid drops. The relevant mathematics is available for the situations with solid particles, for example, or spherical shells. The... And the results show you how to get this algebraic expressions for the correction for the size, instead of referring to the more complicated expressions that involve spherical Bessel and Hankel functions. But it does require that the size not be too large. It has to do with what are the first important corrections to the contrast factor approach. 

Kat Setzer  07:43

Okay.

Philip Marston  07:45

The September article was essentially intended to help readers, again modern readers, understand really what was available in the early approaches, but those were cast in, those were written in terminology that was widely used in, say, physics education, physics graduate education, in my case. And now you have more and more people becoming interested in these applications. They don't necessarily appreciate as well the way those articles were written. So what I tried to do is cast, in some sense, one of the most important results  from that series of articles in a terminology that would be more easily appreciated by modern readers. 

Kat Setzer  08:34

Okay, okay, got it. What approaches did you consider for extending the approximation of the contrast factor. How did you end up testing or validating these approaches?

Philip Marston  08:45

Analytic expressions for radiation force functions predicted a dependence on sphere size not present in the contrast factor approach. Properly understood, the force function approach, which makes use of spherical Bessel and Hankel functions, recovers the contrast factor approach for spheres small in comparison with the wavelength. I should add that support for the radiation force functions was given in the 1970s and 80s by various researchers.

Kat Setzer  09:24

Okay, so what did you end up showing with regards to the contrast factor for standing wave radiation forces on larger spheres?

Philip Marston  09:32

There are potentially significant force corrections when the radius exceeds 1/10 the wavelength, and those are given by simple algebraic series expansions for cases of interest. The value of the algebraic series expansions is that you don't have to refer to the spherical Bessel and Hankel functions, which hide the way the quantities depend upon the relevant acoustical properties. 

Kat Setzer  10:07

Okay, okay, got it. So your most recent article in JASA and moves away from spheres and considers drop-shaped objects. Why?

Philip Marston  10:16

In the late 1970s and early 1980s some analytical approximations were developed for how radiation force alters the shape of drops, and these remain relevant in modern research.

Kat Setzer  10:32

Okay, okay, so what were the findings about how the changes in shape? Why that's relevant? 

Philip Marston  10:39

Broadly speaking, there are two related mechanisms. First, the balance between the spatial distribution of radiation stresses and the surface tension stresses requires the shape to deviate from a sphere. Secondly, as demonstrated in the late 1970s, modulation of the ultrasonic amplitude causes the shape to oscillate in a controlled way at a low frequency. The 1980 era analytic approach included the dependence of the relevant radiation force projection on the location of the drop. But that has been left out of the reviews of early work given in publications appearing since about 1998. An example of a forgotten experiment is that of Xiu and Apfel done at Yale, that's Journal of Acoustical Society in 1985, where shape oscillations were ultrasonically driven in drops as small as 25 micron radius. I recently referenced that paper because I think it had been mostly forgotten. 

Kat Setzer  11:57

Hmm, okay, okay. Why is it problematic to not consider location of the droplet in the standing wave when estimating deformation of the droplet?

Philip Marston  12:08

You could significantly overestimate the deformation in some cases, and if you're using that to infer the surface tension, you'll end up inferring the wrong surface tension. 

Kat Setzer  12:19

Okay. What is the relationship between the steady-state shape of weakly deformed, levitated drops and bubbles on the projections?

Philip Marston  12:28

For static, small deformations, there is a linear relationship between stress projection and the deformation in a way that depends on the surface tension and the radius that was analyzed and published in Journal Acoustical Society in 1980.

Kat Setzer  12:46

Okay. Okay, so how can acoustic radiation pressure driven deformation of drops and bubbles be used?

Philip Marston  12:55

From the late 1970s onward, such deformations have been used to investigate interfacial properties, including modifications introduced by other types of interfacial molecules. A 1981 paper noted the potential relevance to the deformation of biological cells static deformation of levitated drops since 1980 has been used to explore the relationship between shape and light scattering. Since the late 1970s modulated radiation forces have been used to extract dynamical information and also used to break up drops and subsequently were used to break up bubbles.

Kat Setzer  13:45

Oh, okay, got it. So do you have any closing thoughts?

Philip Marston  13:49

Related investigations were developed in parallel with those reviewed here. They concerned the rotation of objects using acoustical and optical radiation forces, the pulling on objects using specialized beams, as well as the response of large objects to modulated radiation forces, and the significance of viscous Stokes layers and acoustic streamings. Those were noted as early as 1980. Related experiments and theories supported by NASA in the 1990s showed how plateau Rayleigh, surface tension instabilities of liquid columns can be suppressed and explored using acoustic radiation pressure. The basic mathematics is similar to those that were developed for the drop problems.

Kat Setzer  14:41

It's been so fun to learn about, not only acoustic levitation, which is a really fascinating concept, but also about how the shift in how research is published has affected the communication about the research to other scientists. I look forward to hearing from you, more from you, and have a great day.

Philip Marston  14:54

Thank you. I think it's appropriate that I acknowledge my research sponsors over some decades, including going back to some of the early work on acoustic deformation, that included the Office of Naval Research and a Sloan Foundation fellowship from the 1990s. A lot of the research was sponsored the by NASA, but there was also some Navy work for understanding the effects on bubbles, on doing bubble dynamics using radiation pressure. And then, more recently, my interest in acoustic radiation forces on large objects is still supported by the Office of Naval Research. Thank you.

Kat Setzer  15:43

Thank you for tuning in to Across Acoustics. If you would like to hear more interviews from our authors about their research, please Subscribe and find us on your preferred podcast platform.