Aerodynamic Leidenfrost effect

When deposited on a plate moving quickly enough, any liquid can levitate as it does when it is volatile on a very hot solid (Leidenfrost effect). In the aerodynamic Leidenfrost situation, air gets inserted between the liquid and the moving solid, a situation that we analyze. We observe two types of entrainment. (i) The thickness of the air gap is found to increase with the plate speed, which is interpreted in the Landau-Levich-Derjaguin frame: Air is dynamically dragged along the surface and its thickness results from a balance between capillary and viscous effects. (ii) Air set in motion by the plate exerts a force on the levitating liquid. We discuss the magnitude of this aerodynamic force and show that it can be exploited to control the liquid and even to drive it against gravity.

Figure 1

Aerodynamic Leidenfrost effect. (a) Schematic of the experimental setup. A drop of viscosity $\eta =96\mathrm{mPa}\mathrm{s}$ and millimeter-size radius $R$ is gently deposited from a syringe on a disk of aluminum rotating at an angular velocity $\omega$. The disk velocity under the drop is denoted by $V$. (b) Side view of a drop of silicone oil (with $R=1.24\mathrm{mm})$ for $\omega =44\mathrm{rad}/\mathrm{s}$ and $V=4\mathrm{m}/\mathrm{s}$ (see movie 1 in Ref. [22]). Levitation is observed, as shown by the nonwetting shape of the drop and by the ray of light between the liquid and its reflection. The disk entrains a boundary layer of thickness $\delta \approx 2.5{({\eta }_a/{\rho }_a\omega )}^{1/2}\approx 1.5\mathrm{mm}$, whose profile is sketched in blue, at the correct scale. Due to the plate motion, the drop drifts at a velocity $u\ll V$. (c) As the plate velocity $V$ increases from 1.5 m/s to 9.7 m/s, the gap thickness also increases (see movies 2–4 in Ref. [22]). Here the drop size is kept constant with $R=1.24\mathrm{mm}$.

Figure 2

Measurements of air gap thickness. (a) Base of a drop of silicone oil $(R=1.24\mathrm{mm})$ levitating above an aluminum plate moving from left to right at $V=3.0\mathrm{m}/\mathrm{s}$. The thickness of air is measured in the flat zone where it is minimum (blue box). In this area, the gray shade of each pixel is measured along the dashed vertical line as a function of the position $z$. (b) Variations of the pixel intensity $I$ as a function of $z$, for five surface velocities $V$. Circles show data and lines are Gaussian fits, whose width provides the thickness $h$. (c) Air thickness $h$ as a function of plate velocity $V$. Black and blue data points correspond to silicone oil and glycerol of radius $R=1.24\mathrm{mm}$ and red data points correspond to bigger drops of glycerol $\left(R=1.68\mathrm{mm}\right)$. Open symbols indicate measurements by Lhuissier et al. [14], performed by colored interferometry through a transparent substrate (for $R=1.16$ and 1.39 mm). (d) A log-log plot of the ratio $h/R$ as a function of the capillary number $\mathrm{Ca}={\eta }_{a}V/\gamma$, with ${\eta }_a$ the air viscosity and $\gamma$ the surface tension of the drop. The open symbol summarizes all the data by Lhuissier et al. [14], obtained at a velocity $V=1.54\pm 0.11\mathrm{m}/\mathrm{s}$ and $R=0.55$, 1.16, and 1.39 mm. The data collapse and they are consistent with the power law $h=0.60R\mathrm{C}{\mathrm{a}}^{2/3}$ represented by a dotted line.

Figure 3

Estimating aerodynamic forces from drop acceleration. (a) Chronophotograph of a drop of silicone oil $(R=1.25\mathrm{cm})$ deposited at 1 cm from the edge of a plate rotating at $V=3.5\mathrm{m}/\mathrm{s}$. Successive images are separated by 12.5 ms. The drop is entrained along a quasistraight line and its position is denoted by $x$. (See movies 5 and 6 in Ref. [22].) (b) Position $x$ as a function of time $t$ for various plate velocities $V$. Thin lines are parabolic fits $x=a{t}^2$, from which we deduce a constant force of entrainment $F=2ma$. (c) Force $F$ as a function of plate velocity $V$, for various drop radii $R$. Lines show Eq. (2) drawn with $\alpha =3$ and $\beta =0.55$. The dotted line is the best fit $(\alpha =1.7$ and $\beta =0.55)$ for the smallest droplet of radius $R=0.7\mathrm{mm}$.

Figure 4

Chronophotograph of a drop of silicone oil $(R=0.94\mathrm{mm})$ dispensed by a needle (on the left) on a surface inclined by an angle of ${22}^{\circ }$ and moving to the right at $V=9\mathrm{m}/\mathrm{s}$. The aerodynamic entrainment force $F$ is large enough to push oil up and accelerate it against gravity. Successive images are separated by 8 ms.