Boundary-layer modeling of polymer-based acoustofluidic devices

In fluid-filled microchannels embedded in solid devices and driven by megahertz ultrasound transducers, the thickness of the viscous boundary layer in the fluid near the confining walls is typically three to four orders of magnitude smaller than the acoustic wavelength and five orders of magnitude smaller than the longest dimension of the device. This large span in length scale renders direct numerical simulations of such devices prohibitively expensive in terms of computer memory requirements, and consequently the so-called boundary-layer models are introduced. In such models, approximate analytical expressions of the boundary-layer fields are found and inserted in the governing equations and boundary conditions for the remaining bulk fields. Since the bulk fields do not vary across the boundary layers, they can be computed numerically using the resulting boundary-layer model without resolving the boundary layers. However, current boundary-layer models are only accurate for hard solids (e.g., glass and silicon) with relatively small oscillation amplitudes of the confining wall, and they fail for soft solids (e.g., polymers) with larger wall oscillations. In this work, we extend the boundary-layer model of Bach and Bruus, J. Acoust. Soc. Am. 144, 766 (2018) to enable accurate simulation of soft-walled devices. The extended model is validated by comparison (1) with direct numerical simulations in three and two dimensions of tiny submillimeter- and larger millimeter-sized polymer devices, respectively, and (2) with previously published experimental data.