Re-examining the boundary conditions in modelling SAW-driven acoustofluidic streaming

Abstract

Numerical simulations of surface acoustic wave (SAW)-induced acoustic streaming are highly sensitive to the choice of second-order boundary conditions. This study systematically compares the no-slip (NS) and Stokes slip (SD) boundary conditions through different numerical approaches. Two- and three-dimensional simulations based on the Reynolds stress method are performed for standing SAW and travelling SAW devices. Results are validated against particle image velocimetry measurements of streaming patterns and velocities. We show that the SD condition yields Lagrangian velocity fields in significantly better agreement with experiments than the NS condition, accurately capturing vortex number, rotation direction, and amplitude across varying device geometries and operating conditions. In contrast, the NS condition overpredicts velocities by 1-2 orders of magnitude and often fails to reproduce experimentally observed vortex structures. These findings highlight the essential role of the Stokes drift boundary condition in modelling acoustic streaming and provide clear guidance for its use in future simulations of SAW-based acoustofluidic systems.

Figures (13)

• Figure 1: (a) Three-dimensional schematic and (b) two-dimensional $x$-$z$ cross-section of the SAW device. (c) Illustration of the fluid domain model used in the simulations.
• Figure 2: Distributions of the normalized absolute acoustic pressure $|p_{1}|/|p_{1\mathrm{max}}|$ and the Lagrangian velocity $\bm{v}^{\mathrm{L}}$ in the channel $x$-$z$ cross-section for the NS and SD boundary conditions. Results are shown for an SSAW device with parameters $h=0.75$, $w=2$, $\lambda_{\mathrm{s}}=200\ \upmu\mathrm{m}$, $\lambda_{\mathrm{v}}=80.7\ \upmu\mathrm{m}$, and vibration amplitude $\xi_{1}=0.3\ \mathrm{nm}$. The first row corresponds to a phase difference $\Delta\phi = 0$; the second row to $\Delta\phi = \pi$. Streamlines depict the flow field; arrows indicate local velocity direction.
• Figure 3: Eulerian velocity $\bm{v}^{\mathrm{E}}$ distributions for the SSAW device ($\Delta\phi=0$) under different modeling approaches: (a) NS condition, (b) SD condition with body force $\bm{F}_{\mathrm{Reynolds}} = 0$, and (c) full SD condition. Streamlines depict the flow field; arrows indicate local velocity direction. Device parameters are identical to those in Fig. \ref{['model_difference_comparison']}.
• Figure 4: Velocity distributions in an SSAW device, obtained near the bottom boundary $\Gamma_{\mathrm{B}}$ within the region $-\lambda_{\mathrm{s}}/2 < x < \lambda_{\mathrm{s}}/2$, $0 < z < 4\delta_\mathrm{v}$: (a) $\bm{v}^{\mathrm{E}}$ under the NS condition and (b) $\bm{v}^{\mathrm{L}}$ under the SD condition. White arrows indicate flow direction. Device parameters match Fig. \ref{['model_difference_comparison']} ($\Delta\phi = 0$).
• Figure 5: Normalized acoustic pressure $|p_1|/|p_{1\mathrm{max}}|$ and Lagrangian velocity $\bm{v}^{\mathrm{L}}$ distributions for TSAW devices with different channel heights $h$, under NS and SD conditions. Wave propagation is along $+x$. Streamlines depict the flow field; arrows indicate local velocity direction. Parameters: $w=4$, $\lambda_{\mathrm{s}}=200\ \upmu\mathrm{m}$, $\lambda_{\mathrm{v}}=80.7\ \upmu\mathrm{m}$, $\xi_1=1\ \mathrm{nm}$.