Asymmetric steady streaming as a mechanism for acoustic propulsion of rigid bodies

Abstract

Recent experiments showed that standing acoustic waves could be exploited to induce selfpropulsion of rigid metallic particles in the direction perpendicular to the acoustic wave. We propose in this paper a physical mechanism for these observations based on the interplay between inertial forces in the fluid and the geometrical asymmetry of the particle shape. We consider an axisymmetric rigid near-sphere oscillating in a quiescent fluid along a direction perpendicular to its symmetry axis. The kinematics of oscillations can be either prescribed or can result dynamically from the presence of an external oscillating velocity field. Steady streaming in the fluid, the inertial rectification of the time-periodic oscillating flow, generates steady stresses on the particle which, in general, do not average to zero, resulting in a finite propulsion speed along the axis of the symmetry of the particle and perpendicular to the oscillation direction. Our derivation of the propulsion speed is obtained at leading order in the Reynolds number and the deviation of the shape from that of a sphere. The results of our model are consistent with the experimental measurements, and more generally explains how time periodic forcing from an acoustic field can be harnessed to generate autonomous motion.

A Force to Be Reckoned With: A Review of Synthetic Microswimmers Powered by Ultrasound

“…The propulsion mechanism of metallic microrods in standing ultrasonic waves was recently examined more closely from a theoretical perspective by Nadal and Lauga . They proposed a new theory based on asymmetric local streaming, and provided a rigid theoretical framework to describe the process by which the small amplitude oscillation of rigid bodies in a standing wave can translate, via shape asymmetry‐induced local acoustic streaming effects, into motion in a direction perpendicular to the acoustic wave.…”

“…Based on their calculation, a roughly spherical particle with an aspect ratio of 10 in a standing acoustic wave could be propelled at ≈26 μm s −1 in conditions similar to those used by a previous group . Although this value is one order of magnitude smaller than the experimentally measured particle speed (up to 200 μm s −1 ), the theoretical framework established by Nadal and Lauga has laid the foundation for a more coherent and accurate theory.…”

“…This interesting phenomenon immediately attracted a significant amount of attention within the scientific community, and have served as the foundation for a series of reports that include preliminary studies of drug delivery with functionalized ultrasound‐powered microswimmers, and activation of ultrasound‐powered microswimmers inside living cells . Furthermore, different theories regarding how ultrasound induces autonomous motion have been proposed . Although both magnetic and ultrasonic propulsion of microswimmers are biocompatible (at appropriate power levels), powering micromachines with MHz ultrasound has a few unique advantages.…”

Synthetic Nano- and Micromachines in Analytical Chemistry: Sensing, Migration, Capture, Delivery, and Separation

“…Other forms of motion driven by self-generated gradients have more recently been demonstrated. For example, motors driven by self-diffusiophoresis (Figure 2b) are propelled by self-generated chemical concentration gradients (60,(76)(77)(78), and self-acoustophoretic motors (Figure 2c) are propelled by asymmetric steady streaming of the fluid around them in an acoustic field (63,(79)(80)(81). Temperature gradients can also be used by microparticles to create motion, a mechanism referred to as self-thermophoresis (65)(66)(67).…”

Wireless actuation with functional acoustic surfaces

“…In the former, the double energy transduction increases the system's complexity and dramatically reduces its efficiency, making this method not suitable for small-scale devices. An example of the second approach is the use of geometrically asymmetric particles and inertial forces in fluids to generate steady stress on the particles, resulting in a finite propulsion speed, which was recently modeled by Lauga et al 12 and experimentally demonstrated by Mallouk et al 13,14 and Wang et al 15,16 A way to increase efficiency, while also enabling control of multiple DoFs, is to exploit acoustic resonances 17 and frequency-division multiplexing. A spherical gas bubble submerged in a liquid, for instance, has a resonant frequency as described by the Rayleigh-Plesset equation, 18 at which large volume oscillation is observed, and fluid streaming away from the bubble is induced.…”