Frequency effects on the scale and behavior of acoustic streaming

Acoustic streaming underpins an exciting range of fluid manipulation phenomena of rapidly growing significance in microfluidics, where the streaming often assumes the form of a steady, laminar jet emanating from the device surface, driven by the attenuation of acoustic energy within the beam of sound propagating through the liquid. The frequencies used to drive such phenomena are often chosen ad hoc to accommodate fabrication and material issues. In this work, we seek a better understanding of the effects of sound frequency and power on acoustic streaming. We present and, using surface acoustic waves, experimentally verify a laminar jet model that is based on the turbulent jet model of Lighthill, which is appropriate for acoustic streaming seen at micro- to nanoscales, between 20 and 936 MHz and over a broad range of input power. Our model eliminates the critically problematic acoustic source singularity present in Lighthill's model, replacing it with a finite emission area and enabling determination of the streaming velocity close to the source. At high acoustic power $P$ (and hence high jet Reynolds numbers ${\mathrm{Re}}_{\mathrm{J}}$ associated with fast streaming), the laminar jet model predicts a one-half power dependence ($U\ensuremath{\sim}{P}^{1/2}\ensuremath{\sim}$ ${\mathrm{Re}}_{\mathrm{J}}$) similar to the turbulent jet model. However, the laminar model may also be applied to jets produced at low powers---and hence low jet Reynolds numbers ${\mathrm{Re}}_{\mathrm{J}}$---where a linear relationship between the beam power and streaming velocity exists: $U\ensuremath{\sim}P\ensuremath{\sim}{\mathrm{Re}}_{\mathrm{J}}^{2}$. The ability of the laminar jet model to predict the acoustic streaming behavior across a broad range of frequencies and power provides a useful tool in the analysis of microfluidics devices, explaining peculiar observations made by several researchers in the literature. In particular, by elucidating the effects of frequency on the scale of acoustically driven flows, we show that the choice of frequency is a vitally important consideration in the design of small-scale devices employing acoustic streaming for microfluidics.