Numerical simulation of micro-particle rotation by the acoustic viscous torque†
We present the first numerical simulation setup for the calculation of the acoustic viscous torque on arbitrarily shaped micro-particles inside general acoustic fields. Under typical experimental conditions, the particle deformation plays a minor role. Therefore, the particle is modeled as a rigid body which is free to perform any time-harmonic and time-averaged translation and rotation. Applying a perturbation approach, the viscoacoustic field around the particle is resolved to obtain the time-averaged driving forces for a subsequent acoustic streaming simulation. For some acoustic fields, the near-boundary streaming around the fluid-suspended particle induces surface forces on the nonrotating particle that integrate into a non-zero acoustic viscous torque. In the equilibrium state, this torque is compensated by an equal and opposite drag torque due to the particle rotation. The rotation-induced flow field is superimposed on the acoustic streaming field to obtain the total fluid motion around the rotating particle. In this work, we only consider cases within the Rayleigh limit even though the presented numerical model is not strictly limited to this regime. After a validation by analytical solutions, the numerical model is applied to challenging experimental cases. For an arbitrary particle density, we consider particle sizes that can be comparable to the viscous boundary layer thickness. This important regime has not been studied before because it lies beyond the validity limits of the available analytical solutions. The detailed numerical analysis in this work predicts nonintuitive phenomena, including an inversion of the rotation direction. Our numerical model opens the door to explore a wide range of experimentally relevant cases, including non-spherical particle rotation. As a step toward application fields such as micro-robotics, the rotation of a prolate ellipsoid is studied.