Acoustic propulsion of a small bottom-heavy sphere

• Main Authors: Nadal, Francois, Michelin, Sebastien
• Format: Journal Article
• Language: English
• Published: 19-05-2020
• Subjects: Physics - Biological Physics; Physics - Fluid Dynamics; Physics - Soft Condensed Matter
• DOI: 10.48550/arxiv.2005.09401

J. Fluid Mech., 2020, 898, A10 We present here a comprehensive derivation for the speed of a small
bottom-heavy sphere forced by a transverse acoustic field and thereby establish
how density inhomogeneities may play a critical role in acoustic propulsion.
The sphere is trapped at the pressure node of a standing wave whose wavelength
is much larger than the sphere diameter. Due to its inhomogeneous density, the
sphere oscillates in translation and rotation relative to the surrounding
fluid. The perturbative flows induced by the sphere's rotation and translation
are shown to generate a rectified inertial flow responsible for a net mean
force on the sphere that is able to propel the particle within the
zero-pressure plane. To avoid an explicit derivation of the streaming flow, the
propulsion speed is computed exactly using a suitable version of the Lorentz
reciprocal theorem. The propulsion speed is shown to scale as the inverse of
the viscosity, the cube of the amplitude of the acoustic field and is a non
trivial function of the acoustic frequency. Interestingly, for some
combinations of the constitutive parameters (fluid to solid density ratio,
moment of inertia and centroid to center of mass distance), the direction of
propulsion is reversed as soon as the frequency of the forcing acoustic field
becomes larger than a certain threshold. The results produced by the model are
compatible with both the observed phenomenology and the orders of magnitude of
the measured velocities.