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 non-vortex excitation at the base, we analyse 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 thickness of the viscous boundary layer. Theoretical predictions align closely with finite element simulations based on a 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.
Marques et al. (Thu,) studied this question.