Inter-Particle Effects with a Large Population in Acoustofluidics

Abstract

The ultrasonic manipulation of cells and bioparticles in a large population is a maturing technology. There is an unmet demand for improved theoretical understanding of the particle–particle interactions at a high concentration. In this study, a semi-analytical method combining the Jacobi–Anger expansion and two-dimensional finite element solution of the scattering problem is proposed to calculate the acoustic radiation forces acting on massive compressible particles. Acoustic interactions on arrangements of up to several tens of particles are investigated. The particle radius ranges from the Rayleigh scattering limit (ka«1) to the Mie scattering region (ka≈1). The results show that the oscillatory spatial distribution of the secondary radiation force is related to the relative size of co-existing particles, not the absolute value (for particles with the same radius). In addition, the acoustic interaction is non-transmissible for a group of identical particles. For a large number of equidistant particles arranged along a line, the critical separation distance for the attraction force decreases as the number of particles increases, but eventually plateaus (for 16 particles). The range of attraction for the formed cluster is stabilized when the number of aggregated particles reaches a certain value.

Acoustofluidic cell micro-dispenser for single cell trajectory control

“…According to the in-depth analytical analysis performed by Jia et al , large particles which are on the order of the acoustic wavelength, will experience stronger secondary acoustic forces, known as inter-particle forces or Bjerknes forces. 66 These inter-particle forces lead to an attractive force between them, resulting in the formation of particle clusters. As the particles approach the acoustic pressure node, the effective range of the inter-particle forces expands, leading to a further increase in the attractive force and subsequently to cluster.…”

“…As the particles approach the acoustic pressure node, the effective range of the inter-particle forces expands, leading to a further increase in the attractive force and subsequently to cluster. 66 The same force, in conjunction with drag forces, is also responsible for the re-organization of the particles within the trapped cluster perpendicular to the pressure barrier as more particles enter and become trapped, which results in the de-centralisation of the cluster with respect to the fluidic channel (refer to ESI † Fig. S4 for time-lapsed images of particle trapping).…”