Modulated exponential films generated by surface acoustic waves and their role in liquid wicking and aerosolization at a pinned drop

The exponentially decaying acoustic pressure of scattered surface acoustic waves (SAWs) at the contact line of a liquid film pinned to filter paper is shown to sustain a high curvature conic tip with micron-sized modulations whose dimension grows exponentially from the tip. The large negative capillary pressure in the film, necessary for offsetting the large positive acoustic pressure at the contact line, also creates significant negative hydrodynamic pressure and robust wicking action through the paper. An asymptotic analysis of this intricate pressure matching between the quasistatic conic film and bulk drop shows that the necessary SAW power to pump liquid from the filter paper and aerosolize, expressed in terms of the acoustic pressure scaled by the drop capillary pressure, grows exponentially with respect to twice the acoustic decay constant multiplied by the drop length, with a universal preexponential coefficient. Global rapid aerosolization occurs at a SAW power twice as high, beyond which the wicking rate saturates.

Figure 1

(a) Schematic of SAW device (side view), where the SAW refracts into the liquid film eluting from the paper at angle ${\theta }_R={22}^{\circ }$. (b) Measurement of fluid pumping velocity. The paper wick is seeded with a slug of red ink, whose position is tracked over time to yield a velocity measurement.

Figure 2

Film regimes under increasing SAW power from left to right. (a)–(c) Quasistable film regime (no aerosol). The inset shows a closeup view of the acoustic droplets and their exponential envelope from the theory. (d)–(f) Weak aerosolization regime. Initial film rupture occurs and droplet emission takes place near the filter paper. The inset shows a discrete aerosolization event. (g)–(i) Rapid aerosolization regime, in which the film has thinned and aerosol emission occurs near the contact line. Numerical solutions are overlaid in yellow and match the topology closely. The filter paper is outlined in red on the left. The working solutions were DI water (top row), acetonitrile (middle row), and 40$\%$ acetic acid-DI water by volume (bottom row).

Figure 3

Phase diagram of SAW-induced liquid film regimes for different nondimensionalized SAW pressures $B^{*}$ and decay constants $k^{*}$. The working solutions, from lowest to highest decay constant, acetonitrile, DI water, 10$\%$ acetic acid-DI water by volume, 40$\%$ acetic acid-DI water by volume, and 11$\%$ glycerol-DI water by volume. Pluses indicate the quasistable film regime (no aerosol), stars indicate the weak aerosolization regime with initial film rupture and droplet emission, and squares indicate the rapid aerosolization regime. The solid blue lines are the numerical phase boundaries. The dashed magenta lines show the $B^{*}\sim \delta e^{2k^{*}\tilde{L}}$ scaling derived via asymptotic analysis, with ${\delta }_{\mathrm{weak}}=1.7$ and ${\delta }_{\mathrm{rapid}}=3.4$ for the weak and rapid aerosolization phase boundaries. The inset collapses the weak aerosolization and rapid aerosolization phase boundaries for $\tilde{L}=1$ to 4 with the same value of ${\delta }_{\mathrm{weak}}$ (${\delta }_{\mathrm{rapid}}$) used for each weak (rapid) aerosolization boundary.

Figure 4

Flow velocity as a function of nondimensionalized SAW pressure $B^{*}$ for DI water. The solid blue curves show theoretical flow velocity and the vertical dashed orange lines show the computed aerosolization regimes. The oblique dashed blue line shifts the onset of SAW pumping to match the onset of weak aerosolization. Inset shows nondimensionalized hydrodynamic pressure $P_o^{*}$ used to calculate the flow velocity via the Ergun equation, as a function of the nondimensionalized decay constant $k^{*}$. Pluses, stars, and squares are used to indicate the quasistable film regime, weak aerosolization regime, and the rapid aerosolization regime, respectively.