Nonlinear hydrodynamic effects induced by Rayleigh surface acoustic wave in sessile droplets

We report an experimental and numerical characterization of three-dimensional acoustic streaming behavior in small droplets of volumes (1–30 µl) induced by surface acoustic wave (SAW). We provide a quantitative evidence of the existence of strong nonlinear nature of the flow inertia in this SAW-driven flow over a range of the newly defined acoustic parameter FNA=F?/(s/Rd)=0.01, which is a measure of the strength of the acoustic force to surface tension, where F is the acoustic body force, ? is the SAW wavelength, s is the surface tension, and Rd is the droplet radius. In contrast to the widely used Stokes model of acoustic streaming, which generally ignores such a nonlinearity, we identify that the full Navier-Stokes equation must be applied to avoid errors up to 93% between the computed streaming velocities and those from experiments as in the nonlinear case. We suggest that the Stokes model is valid only for very small acoustic power of =1 µW (FNA<0.002). Furthermore, we demonstrate that the increase of FNA above 0.45 induces not only internal streaming, but also the deformation of droplets.