Characterization of Acoustic Streaming in Gradients of Density and Compressibility

TL;DR

This paper extends the theory and experiment of acoustic streaming in fluids with spatial inhomogeneities in density and compressibility by introducing solute-driven gradients and tracking their evolution under a standing half-wavelength acoustic field. It demonstrates that the acoustic body force arising from these gradients can suppress bulk streaming, confining vortices to near-wall regions, with the suppression evolving over time as diffusion and advection act on the concentration field. The key findings show that streaming suppression occurs for solute mass fractions down to $0.1\%$, that diffusion dominates early-time evolution of the concentration profile, and that an early-time diffusion scaling collapses multiple data sets when normalized by the appropriate diffusion time, while later advection-diffusion effects cause deviations. The results have implications for acoustophoresis-based manipulation and enrichment of sub-micrometer particles in microfluidic systems, enabling more robust acoustic focusing and separation in inhomogeneous media.

Abstract

Suppression of boundary-driven Rayleigh streaming has recently been demonstrated for fluids of spatial inhomogeneity in density and compressibility owing to the competition between the boundary-layer-induced streaming stress and the inhomogeneity-induced acoustic body force. Here we characterize acoustic streaming by general defocusing particle tracking inside a half-wavelength acoustic resonator filled with two miscible aqueous solutions of different density and speed of sound controlled by the mass fraction of solute molecules. We follow the temporal evolution of the system as the solute molecules become homogenized by diffusion and advection. Acoustic streaming rolls is suppressed in the bulk of the microchannel for 70-200 seconds dependent on the choice of inhomogeneous solutions. From confocal measurements of the concentration field of fluorescently labelled Ficoll solute molecules, we conclude that the temporal evolution of the acoustic streaming depends on the diffusivity and the initial distribution of these molecules. Suppression and deformation of the streaming rolls are observed for inhomogeneities in the solute mass fraction down to 0.1 %.

Figures (10)

• Figure 1: (a) Sketch of the acoustofluidic silicon chip (gray) sealed with a glass lid, which allows optical recording (purple) of the tracer bead motion (red trajectories) in the channel cross section of width $W = 375 \,\textrm{\textmu{}m}$ and height $H = 133 \,\textrm{\textmu{}m}$. A Ficoll solution (dark blue) is injected in the center and laminated by pure water (light blue). The piezoelectric transducer (brown) excites the resonant half-wave pressure field $p_1$ (inset, green) at 2 MHz. (b) Top-view photograph of the chip (dark gray) mounted on the PZT transducer (brown) and placed in its holder (transparent plastic).
• Figure 2: Sketch of the stop-flow mechanism. (a) When the two liquids are injected, the two syringes are connected to the two inlets through the open four-port valve, and the waste is collected through the open two-port valve. (b) To stop the flow, the two inlets are short circuited by closing the four-port valve, and the outlet is blocked by closing the two-port valve. The center outlet is always blocked during the experiment.
• Figure 3: Confocal images in the horizontal $x$-$y$ plane taken of solution S4 with acoustics on at (a) $\tau$ = 5 s, (b) $\tau$ = 55 s, and (c) $\tau$ = 195 s. The yellow lines indicate the locations where $s_\mathrm{cntr}$ and $s_\mathrm{side}$ are measured, which are then used to determine $\hat{\rho}_*$, $\hat{c}_*$, and $\hat{s}_*$, see Eqs. (\ref{['eq:rhoScS']}) and (\ref{['eq:sStarDef']}).
• Figure 4: The time evolution with acoustics present of the concentration profile for solution S4 with FITC-labelled Ficoll molecules deduced from recordings as shown in Fig. \ref{['fig:sDevelopment']}.
• Figure 5: The particle positions (blue points) in the vertical $y$-$z$ cross section of width $W=375~\textrm{\textmu{}m}$ and height $H=133~\textrm{\textmu{}m}$ overlaid from 100 frames between $\tau$ = 20 s and 30 s for the inhomogeneous solutions S1, S2, S3, and S4 listed in Table \ref{['tab:InjectedSolutions']}. The color plot represents the concentration of the solute molecules from low (dark) to high (white).