Enhanced quality factors at resonance in acoustofluidic cavities embedded in matched elastic metamaterials

TL;DR

The paper demonstrates that embedding liquid-filled acoustofluidic cavities in elastic metamaterials with matched coarse-grained moduli can suppress viscous boundary-layer losses and dramatically boost resonance quality factors. A two-pronged approach—analytical guidance for wall-synchronization and COMSOL-based numerical optimization—yields metamaterial designs that raise the $Q$ from roughly $4.3\times10^2$ to about $1.0\times10^5$ (for optimized unit cells), while simultaneously reducing streaming and enhancing acoustic radiation forces. The study shows that synchronized metamaterial cavities can accelerate acoustophoresis by up to four orders of magnitude for submicron particles and enable focusing of 250-nm particles within a few milliseconds, far faster than conventional cavities. These findings suggest a general strategy to overcome boundary-layer dissipation in a broad class of acoustofluidic and MEMS devices, with practical fabrication routes discussed.

Abstract

We show that by embedding liquid-filled acoustofluidic cavities in a metamaterial, the quality factor of the cavity at selected acoustic resonance modes can be enhanced by 2 to 3 orders of magnitude relative to a comparable conventional cavity by matching the coarse-grained elastic moduli of the metamaterial to the acoustic properties of the liquid.

Figures (6)

• Figure 1: A sketch of the model system with its five domains: the solid base $\Omega^\sl_\mathrm{base}$, the fluid channel $\Omega^\mathrm{fl}$, the solid lid $\Omega^\sl_\mathrm{lid}$, and the metamaterial walls $\Omega^\mathrm{mm}_\mathrm{up}$ and $\Omega^\mathrm{mm}_\mathrm{down}$. The green double arrow represents the oscillation amplitude $d_0$ of the lid (green line).
• Figure 2: The geometry of the simulated device with two $(N_y\times N_z)=(4\times8)$ metamaterial arrays of elongated hexagonal unit cells on either side of the fluid channel. The device is actuated on the outer right-most surface (green line) with a time-harmonic uniform displacement amplitude of $d_0$ (green arrows), while all other walls are free to move having zero-stress conditions.
• Figure 3: Simulation results in and near the fluid cavity: Color plots of the pressure field $p_1$ from min (blue) to max (red) in the fluid and of the magnitude $u_1$ from min (blue) to max (yellow) of the displacement field $\bm{u}_1$ in the solid for (a) a conventional rectangular cavity and (b) the optimized cavity using the $5 \times 10$ metamaterial with the hexagonal unit cell defined in Fig. \ref{['fig:model']}. The first-order displacements $\bm{u}_1$ and $\mathrm{i} \omega^{-1}\bm{v}_1$ of the solid and fluid are represented by evenly spaced, deformed lines and arrows. Animated versions of the panels are given in the Supplemental Material Note1.
• Figure 4: (a) Simulated $Q$-factors and acoustic energy density $E_\mathrm{ac}^\mathrm{fl}$ relative to the all-solid reference system (superscript "ref") for increasing numbers of unit cells $N_y$ across the metamaterial regions. (b) The normalized $Q$ factor $Q/Q^\mathrm{ref}$ of the $N_y=5$ cavity plotted against the relative deviation of either $L_1$, $L_2$, or $L_3$ from the optimum.
• Figure 5: Streaming fields $\bm{v}_2$ normalized by the Rayleigh streaming speed $v_2^\mathrm{Rayl}$ inside (a) the reference cavity and (b) the $(N_y, N_z) = (5,10)$ synchronized metamaterial cavity.