Unsteady time-averaged streaming in microfluidics using traveling surface acoustic waves

The acoustic-induced steady motion of fluids in a confined space is understood by the established acoustic streaming theory but buildup of the streaming receives little attention, especially in microfluidics using surface acoustic waves (SAWs). In this work, we experimentally and numerically studied the temporal acoustic and streaming fields excited by a traveling-SAW lasting for a finite time. Based on the perturbation theory for slow streaming, we propose a concept of unsteady time-averaged large-scale streaming, for which the slow variation of flow velocity is detectable in a time-scale much longer than an acoustic period. Theoretical analysis, numerical calculations, and experiments reveal that the buildup time of the acoustic field, within which the acoustic energy reaches the maximum in a SAW-based device, is about N (the electrode number of interdigital transducers) times of the acoustic period T , while buildup of the streaming field is an acoustic momentum diffusion process. The results show that the geometry of the microchannel determines the characteristic size of the flow, giving a square relationship between the channel height h and buildup time of the streaming. For periodic excitation of SAW pulses, we show the distinct behaviors of the unsteady streaming by a phase diagram. A short pulse duration comparable to the buildup time of the acoustic field makes the streaming fluctuate with unobservable magnitude, whereas microscopic and macroscopic fluctuations are observable for an increasing pulse duration. Based on the separation of the buildup times, we also propose a hybrid time–frequency scheme for efficient finite element analysis, which opens a way to design devices with additional functionality in the time domain.