Using Local Concentration to Model the Progress of Acoustophoretic Assembly of Microspheres in Planar Standing Waves

Abstract

Acoustophoretic assembly uses a standing acoustic field to move dispersed small particles into a geometric pattern. The technique relies on the acoustic radiation force (ARF), which arises from the interaction between the acoustic field and the particles, and drives the particles toward the pressure nodes or antinodes of the standing wave. Acoustophoretic assembly shows potential for a wide range of applications, including organizing filler materials in composites, creating metamaterials, and fabricating functional biological tissue. However, the method has not yet been incorporated into large-scale manufacturing processes. One barrier is the incomplete understanding of the assembly process. While an ideal final pattern geometry can be calculated from the acoustic field and material properties, there are currently no widespread metrics for measuring the progress of the pattern formation. As a result, it is difficult to know how long the acoustic field should be applied during manufacturing. Our approach uses the local particle concentration to model the acoustophoretic assembly process in bulk acoustic waves. We show that the time-dependent local particle concentration can be derived from the force balance on the particles and a control volume analysis. The analysis is applied to microspheres in a planar standing wave, and an analytical expression is obtained, which yields a time parameter for pattern assembly and suggests a cutoff time. We then use the local concentration to define measurements for the quality of the assembled microsphere pattern. Experiments were carried out using polystyrene microspheres in a glycerol–water mixture to validate the theoretical results.