High jump of impinged droplets before Leidenfrost state

Unlike the traditionally reported Leidenfrost droplet which only floats on a thin film of vapor, we observe a prominent jump of the impinged droplets in the transition from the contact boiling to the Leidenfrost state. The vapor generation between the droplet and the substrate is vigorous enough to propel the spreading droplet pancake to an anomalous height. The maximum repellent height can be treated as an index of the total transferred energy. Counterintuitively, a stronger vaporization and a higher jump can be generated in the conditions normally considered to be unfavorable to heat transfer, such as a lower substrate temperature, a lower droplet impact velocity, a higher droplet temperature, or a lower thermal conductivity of the deposition on the substrate. Since the total transferred energy is the accumulation of the instantaneous heat flux during the droplet contacting with the substrate, it can be deduced that a longer contact time period is secured in the case of a lower instantaneous heat flux. The inference is supported by our experimental observations. Moreover, the phase diagrams describe the characteristics of the high repellency under different substrate temperatures, droplet subcooling temperatures, and Weber numbers. It allows us to manipulate the droplet jump for the relative applications.

Figure 1

The schematic of the experimental setup. The inset is the photograph of the droplet train generation, which was captured by the high-speed camera.

Figure 2

(a) and (b) The high repellency of the impinged droplets on the heated substrate (see the evolution of droplet No. 2) and the consequent droplet interactions. The illustrative diagram and the captured images regarding the evolution of the droplet-film interaction in one cycle. Due to the periodical nature, the next phase of droplet No. 2 in (v) repeats the scenario of droplet No. 1 in (i). The corresponding movie is available in the Supplemental Material [28] ($f=28000\mathrm{Hz}$, image 150 000 fps). (c) The high jump can be generated without the film penetration.

Figure 3

The droplet repellency strongly depends on the substrate temperature, whereas the spreading is almost independent of the wall temperature. (a) A higher substrate temperature results in a lower rebound height. (b) The evolution of the spreading diameter follows the simplified Wagner's law $D\sim \sqrt{t}$. The corresponding movie is available in the Supplemental Material [29].

Figure 4

(a) The identified three regimes: contact boiling (I), high repellency (II), and thin-film levitation (III). (b) Variation of $H_m$ as a function of $T_w$ in the baseline test.

Figure 5

The phase diagrams reveal the boundaries of the different regimes in the plot of $T_w$ as a function of (a) $\mathrm{\Delta }{T}_{\mathrm{sub}}$ and (b) We. (c) $T_w$ versus $H_m$ as $\mathrm{\Delta }{T}_{\mathrm{sub}}$ is $-54{}^{\circ }\mathrm{C},-70{}^{\circ }$, or $-75{}^{\circ }\mathrm{C}$. (d) $T_w$ versus $H_m$ as We is 218, 326, or 562.

Figure 6

(a) The high repellency is only observed on the surface in Zone A rather than Zone B. Once the droplet impacts on the boundary, a partial rebound can be found. Please see the corresponding movie in the Supplemental Material [34]. (b) The measurement of the scanning electron microscope (SEM) and energy-dispersive x-ray spectroscopy (EDS) with the embedded atomic percentage.

Figure 7

The proposed explanation for the transition of the repellent height. By assuming that the instantaneous heat transfer $\dot{q}A$ is proportional to the wall superheat, a longer $t_c$ is anticipated in the case of a lower $T_w$ (with a smaller $\dot{q}A$) to transfer sufficient energy $Q_d={\int }_0^{t_c}\dot{q}Adt$ for the repellency.

Figure 8

From the captured images at 680 000 fps, it is proved that the contact time $t_c$ is shorter on a substrate with a higher $T_w$. Point A represents the time that the vapor pockets are observed, whereas Point B is the end time of the contact.