Periodic particle arrangements using standing acoustic waves

TL;DR

This paper presents a method to create crystal-like particle arrangements in liquids using standing acoustic waves, predicting their configurations through eigenvalue analysis of the acoustic potential.

Contribution

It introduces a novel approach to predict and design periodic particle arrangements by analyzing the eigenstructure of acoustic radiation potentials.

Findings

Global minima of acoustic potentials can be predicted by eigenvalues of a symmetric matrix.

Symmetries in eigenvectors relate to specific particle arrangements like points, lines, or planes.

The periodicity of arrangements is limited to certain Bravais lattice classes in 2D and 3D.

Abstract

We determine crystal-like materials that can be fabricated by using a standing acoustic wave to arrange small particles in a non-viscous liquid resin, which is cured afterwards to keep the particles in the desired locations. For identical spherical particles with the same physical properties and small compared to the wavelength, the locations where the particles are trapped correspond to the minima of an acoustic radiation potential which describes the net forces that a particle is subject to. We show that the global minima of spatially periodic acoustic radiation potentials can be predicted by the eigenspace of a small real symmetric matrix corresponding to its smallest eigenvalue. We relate symmetries of this eigenspace to particle arrangements composed of points, lines or planes. Since waves are used to generate the particle arrangements, the arrangement's periodicity is limited to certain Bravais lattice classes that we enumerate in two and three dimensions.