Aerodynamic repellency of impacting liquids

Impacting liquids can be reflected by moving solid plates, provided the surface is fast enough. We describe and model here the threshold speed of bouncing, in particular as a function of the impact velocity of the incoming liquid. We also demonstrate that the aerodynamic force responsible for the nonwetting behavior induces an oblique rebound, which contributes to the liquid removal. In summary, this situation repels viscous, low surface tension drops of any size, all kinds of cases where repellency is impossible to achieve by other means.

Figure 1

(a) Experimental setup. A drop with radius $R$ impacts at velocity $U$ a rotating aluminum plate moving at $V=L\omega$ at the impact point. (b) Chronophotography showing successive images (separated by 6.6 ms) of a drop of silicone oil ($R=0.75\mathrm{mm}$) impinging at $U=0.37\mathrm{m}/\mathrm{s}$ a plate moving at $V=17\mathrm{m}/\mathrm{s}$. The thickness δ of the boundary layer of air is indicated to scale with a dotted line. The corresponding movie is movie 1, see Ref. [22].

Figure 2

Behavior of silicone oil ($R=0.9\mathrm{mm}, \eta =96\mathrm{mPa}\mathrm{s}, \gamma =21\mathrm{mN}/\mathrm{m}, \rho =960\mathrm{kg}/{\mathrm{m}}^3$) impacting at a velocity $U$ a plate moving horizontally at a speed $V$. Origin of time $t$ is chosen when the oil-plate gap is minimum. (a) For $U=0.3\mathrm{m}/\mathrm{s}$ and $V=5\mathrm{m}/\mathrm{s}$, the drop contacts the solid and spreads. The corresponding movie is movie 2, see Ref. [22]. (b) For $U=0.3\mathrm{m}/\mathrm{s}$ and $V=20\mathrm{m}/\mathrm{s}$, the drop bounces and obliquely takes off. The corresponding movie is movie 3, see Ref. [22]. At such drop velocity $U$, bouncing occurs for $V>V^{*}=11\mathrm{m}/\mathrm{s}$. (c) Phase diagram of repellency: red dots show when drops stick to the plate [as shown in Fig. 2], while blue dots and the gray zone indicate that drops bounce [as shown in Fig. 2]. Black circles mark the transition between contact and repellency. For each $U$, five to 10 series of experiments were performed to minimize the error bars.

Figure 3

(a) Drop of silicone oil ($R=0.91\mathrm{mm}$) at $t=-0.1\mathrm{ms}$ for $U=0.29\mathrm{m}/\mathrm{s}$ and $V=38\mathrm{m}/\mathrm{s}$. The drop is deformed by the lateral wind carried by the boundary layer whose thickness $\delta \approx 2.5{\left({\eta }_{\mathrm{a}}L/{\rho }_{\mathrm{a}}V\right)}^{1/2}$ here is 500 μm (dotted line). Air exerts a dynamic pressure, which reshapes the drop base. The induced force $F$ allows the drop to bounce. The corresponding movie is movie 5, see Ref. [22]. (b) Threshold velocity of repellency V* as a function of the impact velocity U, for oil drops with radius $R$ between 0.7 and 1.54 mm. Dotted lines show Eq. (1)), with numerical prefactor $\alpha =0.57$.

Figure 4

(a) Side view of the center of mass of a drop ($U=0.37\mathrm{m}/\mathrm{s}, R=0.75\mathrm{mm}, V=17\mathrm{m}/\mathrm{s}$) showing its first two rebounds. (b) Top view of the rotating disk: drops dispensed 1 cm from the edge of the disk move along an axis denoted as $x$ with a horizontal velocity $u_x$. (c) Velocity $u_x$ of oil as a function of time $t$. At each impact (with duration τ of about 6 ms), the liquid is accelerated by an amount $\mathrm{\Delta }{u}_x\sim 0.2\mathrm{m}/\mathrm{s}$.

Figure 5

(a) Images separated by 3.3 ms of a droplet of silicone oil ($R=0.34\mathrm{mm}$) hitting at $U=0.6\mathrm{m}/\mathrm{s}$ a plate moving at $V=17\mathrm{m}/\mathrm{s}$. In the limit $2R<\delta =0.75\mathrm{mm}$, the velocity $\mathrm{\Delta }{u}_x$ gained after the shock is much larger than previously, as seen from the increased distance between successive positions after take-off. $\mathrm{\Delta }{u}_x$ here is ∼0.5 m/s, instead of ∼0.2 m/s in Fig. 4. The inset shows a zoomed-in picture of oil just before impact: even drops smaller than the boundary layer are asymmetrically deformed. The corresponding movie is movie 9, see Ref. [22]. (b) Increment $\mathrm{\Delta }{u}_x$ in horizontal velocity at impact as a function of $R$, for $U=0.44\pm 0.16\mathrm{m}/\mathrm{s}$ and $V=17\mathrm{m}/\mathrm{s}$. $\mathrm{\Delta }{u}_x$ can be fitted by a hyperbola (thin solid line) of equation $\mathrm{\Delta }{u}_x=D/R$, with $D=1.6\mathrm{c}{\mathrm{m}}^2/\mathrm{s}$, which we discuss in the text.