Quantification of surface acoustic wave induced chaotic mixing-flows in microfluidic wells

We report the use of 20 MHz surface acoustic waves (SAWs) on lithium niobate (LiNbO3) chips to generate fast mixing flows in microfluidic wells. Whilst the chaotic nature of these SAW-driven flows have been speculated in the past, we provide quantitative evidence of the existence of such chaotic advection in these systems over a range of viscosities and input powers through the estimation of the finite time Lyapunov exponent (FTLE), which is a measure of the strength of the chaotic flow. The strongest mixing flows were most evident at higher SAW excitation amplitudes, as expected, since the increasing amounts of inertia in the system served to amplify disturbances in the system that promote the random stretching and folding of the fluid elements over a cascade of length scales in a way that introduces criss-crossing of the streamlines. What is less expected, however, is the effect of fluid viscosity. In contrast to classical acoustic streaming theories where the increase in viscous dissipation is offset by the intensification of the streaming due to increased acoustic energy absorption in systems with larger viscosities, we observe that increases in viscosity essentially suppresses the chaotic advection and hence the mixing effect, which is more akin to most other flow systems. This can be attributed to nonlinear effects due to convective acceleration that cannot be neglected in the fast streaming flows induced at the high MHz frequencies associated with the SAWs. The evidence of the chaotic advection in these SAW-driven flows is further verified through a pixel intensity analysis, in which mixing times, quantified through a normalised mixing index, were observed to be inversely proportional to the Lyapunov exponent, characteristic of processes in which transport is dominated by chaotic advection. Practically, these results, which show mixing events taking place in just seconds, demonstrate the utility of SAWs for the design of effective microfluidic mixers.