Acoustofluidics: Theory and simulation of streaming and radiation forces at ultrasound resonances in microfluidic devices

During the past few years, there has been an increasing interest in applying ultrasound waves to manipulate biological particles and liquids in microfluidic devices. To obtain optimized designs and functionalities of the acoustofluidic devices, more detailed theoretical studies and numerical simulations are called for. The basic second-order perturbation theory is presented for acoustic fields applied at ultrasound frequencies in silicon/glass systems containing water-filled microfluidic channels and chambers. For various specific device geometries, the resonance frequencies and corresponding modes of the acoustic fields are calculated numerically to first order. At these frequencies, the largest possible acoustic powers are obtained in the microfluidic system. The first order fields are then used as source terms in the equations for the time-averaged second order pressure and velocity fields, which are directly related to the acoustic radiation force on single particles and to the acoustic streaming of the liquid. For the radiation pressure effects, there is good agreement between theory and simulation, while the numeric results for the acoustic streaming effects are more problematic. Possible improvements in the latter case are discussed.