2013: Research highlights from the Faculty of Physics  
"Acoustic radiation force"

Collaborative research of physicists from Moscow State University and the University of Washington open new prospects for the use of the ultrasonic radiation force.

Waves of any nature carry not only energy, but also momentum. Radiation force is a result of a change in wave momentum due to scattering at an obstacle. The rate of momentum change, averaged over the wave period, equals the radiation force. This force is well known to physicists, particularly in relation to optical waves. Its magnitude is easy to estimate using quantum language, presenting light as a flux of photons with energy hω and momentum hk=hω/c. These simple expressions show that the radiation force is proportional to the power of the wave, and in the case of one-dimensional propagation the proportionality factor is 1/c, where с is the wave speed. The speed of light is fairly large, so that the corresponding radiation force is relatively small. The first who experimentally measured the optical radiation force (in the late 19th century) was famous Russian scientist P.N. Lebedev, whose monument is located at the entrance to the Physics Faculty of MSU. With the advent of lasers it has become possible to obtain sufficiently intense light beams, and thus it has become relatively easy to create noticeable radiation force on the obstacles. In particular, modern optical tweezers are based on this principle.

And what can be said about radiation force of acoustic waves? It is noteworthy that the aforementioned factor 1/c for sound is approximately 5 orders of magnitude greater than the corresponding factor for light, i.e., generating a noticeable radiation force is much easier. One of the most vivid demonstrations of manifestation of the effect of the radiation force is the "acoustic fountain" -- the emergence of a hydrodynamic jet on the surface of a fluid when an ultrasonic beam is focused on that surface (see photo). Another example is the method of measuring the total power of ultrasonic sources by "weighting" of the emitted beam: ultrasound is directed to an absorber that lies on an electronic balance; the radiation force results in a noticeable change of the absorber weight, which thus allows to measure the total power of the incident wave. The radiation force makes it possible to realize the levitation of small particles and microbubbles. Another illustration of the effect is excitation of the hydrodynamic flow (the so-called acoustic streaming) by an ultrasonic beam that is absorbed in liquid. Similarly, shear waves can be excited in a gel-like material. The possibility of remote excitation of shear waves has already found application in medicine for ultrasound diagnostics of tumor formation in soft biological tissues.

As is often the case, a simplified description helps to understand the cause of the phenomenon, but it is not always possible to describe the effect quantitatively. Such is the situation with the calculation of the acoustic radiation force for real beams and real scattering objects. Until recently, the solution to the problems was possible only under simplifying assumption of one-dimensional nature of the waves or small scatterer size as compared to the wavelength. A rigorous calculation of the radiation force requires the ability to solve the three-dimensional scattering problem, and then use this solution to calculate the radiation force by integrating the radiation stress tensor on any fixed surface enclosing the scatterer. In early 2013, Dr. Oleg Sapozhnikov (Department of Acoustics, Physics Faculty, MSU) and Dr. Michael Bailey (Applied Physics Laboratory, University of Washington, USA) have published a paper in the Journal of the Acoustical Society of America, where they developed an analytical method for the calculation of the radiation force of an arbitrary acoustic beam on an elastic sphere of arbitrary size in a fluid. The authors have not only developed an efficient method of calculating the radiation force, but also used it to describe the forces that can be applied to kidney stones in the human body when using ultrasonic sources in the form of multi-element diagnostic arrays. It was found that the ultrasonic beam can be used not only to push the stone along the ultrasound beam, but also in other directions. This shows that it is possible to remotely manipulate kidney stones. In particular, it is possible to push the small stones to the exit of the patient kidney, and the large stones, on the contrary, can be pushed back in the kidney in order to avoid blockage of the ureter. This approach has already caused enormous interest among urologists, and work is currently being performed to create a medical device based on the effect of the radiation force.

The results of the work have been published in the paper: Sapozhnikov, O.A., and Bailey, M.R. Radiation force of an arbitrary acoustic beam on an elastic sphere in a fluid. – J. Acoust. Soc. Am.,  v. 133, no. 2, pp. 661-676 (2013).