Theoretical analysis of acoustic separation characteristics in rayleigh/mie channel within a standing acoustic wave

Acoustic tweezers provide a versatile approach for contactless particle manipulation by harnessing acoustic radiation forces with acoustic-streaming-induced transport. Although the size-dependent competition between these two mechanisms is well established, the extent to which their force balance is governed by the relationship between the characteristic size of the liquid domain and the acoustic wavelength remains insufficiently quantified. In this paper, we conduct a theoretical and numerical analysis of the acoustic pressure distribution, streaming flow, and particle dynamics based on the bulk acoustic standing wave system in Rayleigh/ Mie-scale liquid domains under different droplet sizes, excitation frequencies, and boundary geometries. Furthermore, we precisely analyzed the acoustic driving forces of a single particle in the time domain as well as the steady-state spatial distribution of that particle, and thereby obtained the spatial average force within the channel. Further research indicates that particles with a diameter greater than 10 μm could be effectively captured at the pressure nodes and form high-density aggregation particle bands. The full-space average acoustic force analysis in Rayleigh/Mie-scale channels shows that the critical particle size is approximately 5-10 μm for a balance state with streaming-induced acoustic drag force and acoustic radiation force. Among these, we found that the resonance caused by the channel size structure also has a significant effect on the arrangement of the particles. These findings can provide a theoretical basis for the design of pre-designed channels for acoustic microfluidics targeting specific-sized particles, thereby offering significant support for clinical analyses of biological particle movement, targeted drug therapy, and diagnostic and therapeutic procedures.