Powerful Acoustogeometric Streaming from Dynamic Geometric Nonlinearity

Past forms of acoustic streaming, named after their progenitors Eckart (1948), Schlichting (1932), and Rayleigh (1884), serve to describe fluid and particle transport phenomena from the macro to micro-scale. Governed by the fluid viscosity, traditional acoustic streaming arises from second-order nonlinear coupling between the fluid’s density and particle velocity, with the first-order acoustic wave time averaging to zero. We describe a form of acoustogeometric streaming that has a nonzero first-order contribution. Experimentally discovered in nanochannels of a height commensurate with the viscous penetration depth of the fluid in the channel, it arises from nonlinear interactions between the surrounding channel deformation and the leading order acoustic pressure field, generating flow pressures three orders of magnitude greater than any known acoustically mediated mechanism. It enables the propulsion of fluids against significant Laplace pressure, sufficient to produce $6\mathrm{mm}/\mathrm{s}$ flow in a 130–150 nm tall nanoslit. We find quantitative agreement between theory and experiment across a variety of fluids and conditions, and identify the maximum flow rate with a channel height 1.59 times the viscous penetration depth.

Figure 1

An (a) IDT with a $625\mu \mathrm{m}$ wide aperture produces SAW that propagates (b) underneath an aligned, 1-mm wide, 5-mm long nanoslit etched into the LN substrate with a room-temperature bonded LN cover. Absorbers eliminate reflected waves. The channel depth is greatly exaggerated for clarity. (c) A $20\text{−}\mu \mathrm{m}$ wide, $500\text{−}\mu \mathrm{m}$ long side channel, which controls the filling rate, connects the main channel at 45° to the 1-mm diameter inlet well. A 1-mm diameter (c1) outlet present at the end of the nanoslit distal from the IDT provides a means for (c2) fluid outflow. A (d) side view of the nanoslit indicates the geometry used in the model.

Figure 2

(a),(b),(c) Fluid transport and meniscus dewetting of deionized water from within a 150 nm-thick hydrophilic nanoslit using $\sim 1\mathrm{W}$, 38.5 MHz SAW, and applied from 0 ms. Scale bar: 0.5 mm. With different fluids, the meniscus velocity versus the applied power, (d) nondimensionalized using Eq. (5), where $U_0=1\mathrm{m}/\mathrm{s}$ is the scaled velocity, collapses the onto a line from the (e) original dimensional results. The theory is effective in representing the observed phenomena. Drainage of other fluids, videos, and a version of (e) dimensional fluid velocity versus applied power with error bars are all in the Supplemental Material [25]. Error bars indicate the max-min range of the data for each point ($N\ge 10$).

Figure 3

(a) The $H=150\mathrm{nm}$ nanoslit and IDT generating 38.5-MHz SAW from left to right with 1 W input power. An LDV-measured SAW velocity amplitude contour plot is shown before it propagates underneath the nanoslit. The color bar showing normalized SAW particle velocity amplitude from 0 to 1 is presented on the right of the image. Because of the scale, image stitching was necessary with *boundaries indicated. The initial (b) dewetting of the fluid—water in this case, see Table 1 for dimensions and details—from the edge of the nanoslit by SAW illustrates the effect of near-field Fresnel diffraction. This evolves to a (c) steady-state meniscus deformation into the nanoslit at 394 mW, the depth of which depends on the SAW amplitude. Increasing the SAW power, to 830 mW, (d) drains the water along the entire length of the nanoslit. In (e) the intensity of the SAW ($\propto U^2$) is plotted across the width of the IDT aperture, indicating why there is a (c),(d) narrow channel of flow: the flow is most significant where the SAW intensity is large. Scale bar: 0.2 mm.