First-principle simulation of the acoustic radiation force on microparticles in ultrasonic standing waves

The recent development in the field of microparticle acoustophoresis in microsystems has led to an increased need for more accurate theoretical predictions for the acoustic radiation force on a single microparticle in an ultrasonic standing wave. Increasingly detailed analytical solutions of this specific problem can be found in the literature [Settnes and Bruus, Phys. Rev. E 85, 016327 (2012), and references therein], but none have included the complete contribution from thermoviscous effects. Here, we solve this problem numerically by applying a finite-element method to solve directly the mass (continuity), momentum (Navier-Stokes), and energy conservation equations using perturbation theory to second order in the imposed time-harmonic ultrasound field. In a two-stage calculation, we first solve the first-order equations resolving the thermoviscous boundary layer surrounding the microparticle and with a perfectly matched layer as a non-reflecting boundary condition for the scattered waves. These first-order solutions are then used as source-terms for solving the time-averaged second-order equations [Muller et al., Lab Chip 12, 4617 (2012)] and in particular to determine the second-order time-averaged hydrodynamic stress on the particle surface. From this, we deduce the radiation force and compare it as a function of the physical parameters to existing analytical results.