Vortex Modes in Acoustofluidic Cylindrical Resonators

TL;DR

This paper provides a theoretical analysis of vortex modes in acoustofluidic cylindrical resonators, revealing how different modes generate specific spin angular momentum components and scale with shear wave number, with implications for particle control.

Contribution

It introduces a comprehensive theoretical framework for vortex modes in cylindrical resonators, including nonlinear interactions and validation with finite element simulations.

Findings

Single vortex modes produce axial spin angular momentum.

Dual modes create transverse spin components.

Nonlinear acoustic fields scale with the square of shear wave number.

Abstract

This paper presents a theoretical investigation of vortex modes in acoustofluidic cylindrical resonators with rigid boundaries and viscous fluids. By solving the Helmholtz equation for linear pressure, incorporating boundary conditions that account for no-slip surfaces and vortex and nonvortex excitation at the base, we analyze both single- and dual-eigenfunction modes near system resonance. The results demonstrate that single vortex modes generate spin angular momentum exclusively along the axial direction, while dual modes introduce a transverse spin component due to the nonlinear interaction between axial and transverse ultrasonic waves, even in the absence of vortex excitation. We find that nonlinear acoustic fields, including energy density, radiation force potential, and spin, scale with the square of the shear wave number, defined as the ratio of the cavity radius to the boundary layer depth. Theoretical predictions align closely with finite element simulations based on a thermoviscous model for an acoustofluidic cavity with adiabatic and rigid walls. These findings hold particular significance for acoustofluidic systems, offering potential applications in the precise control of cells and microparticles.