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 mu l) 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 F-NA = F lambda/(sigma/R-d) >= 0.01, which is a measure of the strength of the acoustic force to surface tension, where F is the acoustic body force, lambda is the SAW wavelength, sigma is the surface tension, and R-d 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 mu W (F-NA < 0.002). Furthermore, we demonstrate that the increase of F-NA above 0.45 induces not only internal streaming, but also the deformation of droplets.