Particles or cells in suspension and exposed to ultrasonic waves experience an acoustic radiation force (FR) which, under certain conditions, drives them toward positions of acoustic equilibrium. In this paper, we present a three-dimensional model of the particle motions within the acoustic field generated by ultrasonic standing waves. This model allows a theoretical study of the three-dimensional FR induced by a standing acoustic wave in a microfluidic chamber with rectangular geometry on micrometer-sized spherical particles. The approach models the agglomeration process and the behavior of particle clusters in the acoustic field. To achieve this, expressions for the 3D FR are obtained as the time-average of a gradient of the acoustic potential established within the chamber with two different sets of boundary conditions. The particle motion under the action of this force was analyzed assuming a non-viscous fluid and a particle size much smaller than the acoustic wavelength. The 3D force expressions were used in a simulation employing an optimized Forest–Ruth algorithm to derive the dynamics of N spherical particles. This work provides novel results that predict some particle motion toward chamber or channel walls and the formation of pearl-chain aggregates within channels. These particle movements and the aggregate formation process were observed experimentally in an acoustic device built to assess the validity of the theoretical predictions.
Keywords: Standing waves; Ultrasonic; Acoustic radiation force; Optimized Forest–Ruth algorithm
This research was supported and funded by the Institute of Physical Technologies and Information ITEFI-CSIC, España, through project COOPA20348, I-COOP+2018 and by the Administrative Department of Science, Technology and Innovation of Colombia , Colciencias, through project 222856 933541, conv. 569-2012. We thank Dr. Michael Delay, IDEX Health & Science (Semrock), for comments, suggestions, and assistance with the manuscript.
