Analytical solutions for three-dimensional flow fields actuated by standing surface acoustic waves

This study develops a general theory for analysing a three-dimensional (3-D) acoustofluidic system, which consists of a cavity sandwiched by parallel piezoelectric substrates. The cavity is filled with a fluid and microparticle mixture, whose movements are actuated by surface acoustic waves (SAW) generated by the piezoelectric substrates. In contrast to the formulations based on the velocity potential and streamfunction, we developed a frequency-domain perturbation method to solve the compressible Navier–Stokes equations to obtain the acoustofluidic fields for both inviscid and viscous fluids. These solutions allow for the accurate prediction of the pressure nodal positions within the sandwiched cavity, and the effects of the microfluidic cavity geometry on the pressure nodal position are examined. Our analysis shows that the in-plane pressure-node distribution is controlled by phase modulation, whereas the out-of-plane distribution is governed by the amplitude ratio of the standing SAWs produced by the two parallel substrates. For viscous fluids, a coordinated amplitude–phase modulation strategy is proposed to achieve the desirable wave node distribution. The present theoretical derivations are validated against numerical simulations and laboratory experiments, in terms of both the velocity and pressure fields. This work provides guidelines for the fabrication and operation of acoustofluidic devices, extending current 2-D acoustic control to fully 3-D manipulation of microparticles suspended in the fluid.