Size-Dependent Acoustophoresis in Rectangular Microchannels: Critical Particle Radius and Multidimensional Field Coupling Effects.

Particle manipulation using acoustophoresis has emerged as a pivotal technology in microsystems engineering, garnering significant attention across soft matter physics, biomedical diagnostics, and lab-on-a-chip applications. The operational efficacy of acoustofluidic tweezers platforms hinges on the precise control of the critical particle size threshold that governs the transition between radiation-force-dominated trapping and streaming-mediated transport. Through systematic numerical investigations in rectangular microchannels with two-dimensional (2D) confinement, this study establishes quantitative correlations between critical radius thresholds and geometric parameters in coupled standing-wave fields. The critical radius $r_p^c$ demarcates two distinct transport regimes: (i) Supercritical particles ( $r_p>r_p^c$ ) achieve stable nodal trapping via dominant radiation forces, independent of initial spatial distribution; (ii) subcritical particles ( ) undergo continuous advection through streaming vortices. Our multiphysics framework combines finite element modeling with analytical validation through boundary-layer force equilibrium analysis, revealing three key findings: First, geometric confinement induces characteristic scaling laws ( $r_p^c\propto \sqrt{l}$ with $l$ being the channel size) for one-dimensional (1D) standing waves, confirmed through parametric studies ( $l$ : 0.1-5.1 mm). Second, 1D models maintain predictive accuracy (with discrepancies ) for systems with wavelength ratios ${\lambda }_y/{\lambda }_x>4$ or , but fail in coupled-mode fields ( ) where maximum discrepancies reach $\gamma \approx 63\%$ . Third, orthogonal wave superposition in 2D configurations reduces $r_p^c$ by suppressing streaming velocities, particularly at ${\lambda }_y={\lambda }_x$ . These insights advance fundamental understanding of size-selective acoustophoresis while providing engineering guidelines for performance optimization in acoustic tweezers design.