Transient dynamics in drop impact on a superheated surface

When a drop impinges on a superheated surface, a Leidenfrost vapor layer forms between the drop and the surface. Transient dynamics of the layer can play a critical role for cooling in power plants but is not fully understood. Here we successfully visualize transient dynamics of the layer using ultrafast x-ray imaging. We reveal that a vapor disk with a homogeneous thickness, developed during drop impact, grows in thickness following the Fourier law. At a certain thickness (12 ± 2 μm in this study) of the vapor disk, ripples generate at its periphery due to capillary waves, resulting in significant enhancement of drop vaporization.

Figure 1

Ultrafast x-ray imaging for a Leidenfrost vapor layer during drop impact. (a) Schematic of ultrafast x-ray imaging setup for drop impact. (b) Sequential x-ray images, taken from the blue dashed box region of panel (a) in ethanol drop impact from 4 cm height on a heated substrate $\left(T_s=590{}^{\circ }\mathrm{C}\right)$, showing transient dynamics of a vapor layer (see Supplemental Movie 1 [21]). Interfacial boundaries between the drop and the vapor layer are clearly resolved. (c) Illustration of the transient dynamics of the vapor layer during drop impact. Here the time at the impact moment is set to $t=0$. Scale bar, 100 μm.

Figure 2

Transient dynamics of the vapor layers. Representative x-ray snapshot images for ethanol drops at 4 cm height for different substrate temperatures $\left(T_s\right)$. Ripples are always generated and propagated to the center while growing in amplitude, as marked by orange arrow heads, for all substrate temperatures tested. Scale bar, 100 μm.

Figure 3

Growth of the vapor disks for various substrate temperatures $\left(T_s\right)$. (a) Representative x-ray snapshot images of the vapor disks for different substrate temperatures, taken from the blue dashed box region (Fig. 1) in ethanol drop impact from 4 cm height. Scale bar, 100 μm. (b) Vapor disk thickness (δ) vs $t^{0.5}$ for various substrate temperatures $\left(T_s\right)$. The dashed lines, the best linear fitted ones, show that disk thicknesses grow with $t^{0.5}$ regardless of $T_s$. The error bars are S.D. from 5 to 10 sets of the image data. (c) Illustration of vapor flows through a vapor disk. The thickness growth rate is determined by $Q_v$ (vaporization rate at the liquid-vapor interface, red arrows) minus $Q_{\mathrm{out}}$ (vapor flow rate out of the disk edge, blue arrows). (d) Vapor disk thickness normalized by $t^{0.5}\mathrm{v}\mathrm{s}\mathrm{\Delta }{T}^{0.5}[\mathrm{\Delta }T$: the difference between $T_s$ and $T_b$ (the liquid boiling point)]. The best fit of the slope is $4\times {10}^{-5}\mathrm{m}/{\mathrm{s}}^{0.5}/{\mathrm{K}}^{0.5}$.

Figure 4

Vapor disk growth in rippling. (a) Vapor disk thickness vs $t$ in ethanol drop impact from 4 cm height on a heated substrate $\left(T_s=590{}^{\circ }\mathrm{C}\right)$. After rippling, the disk thickness is lower than estimated (black dashed line) by the Fourier law [δ equation: Eq. (6)]. (b) Rippling thickness $\left({\delta }_r\right)$ is invariant with $\mathrm{\Delta }T\left(=T_s–T_b\right)$. Dashed line represents the average value of each datum, 12 ± 2 μm. (c) Rippling time $\left(t_r\right)$ is inversely proportional to ΔT. (d) $h_L$ (the height of the liquid layer, red diamond) and ${\delta }_r$ (the rippling thickness of the vapor disk, blue circle) vs $U_o$ (impact velocity) when the ripples are generated. ${\delta }_r$ is invariant with $U_o$ while $h_L$ drastically changes.

Figure 5

Onset of capillary waves. Onsets of two types of capillary waves at the top air-liquid (red circle) and the bottom liquid-vapor (blue hexagon) interfaces as a function of $\mathrm{\Delta }T\left(=T_s–T_b\right)$. The onset of capillary waves at the bottom interface is always delayed compared to that at the top interface, and the time lag is getting smaller with Δ$T$.

Figure 6

Group velocity and wavelength of capillary waves. (a) Comparison of the group velocity measured (red squares) to those calculated (blue circles) assuming capillary waves in ethanol drop impact for various impact velocities $(U_0=\sqrt{2gH},g$ is acceleration, and $H$ is the impact height). The dashed line is the linear fit of the measured data. The inset shows the group velocities measured, which are invariant with $\mathrm{\Delta }T$. (b) The wavelength of the ripples $\left(\lambda \right)$, measured as the distance between their first and second peaks, is linearly proportional to $\mathrm{W}{\mathrm{e}}^{-1}$ regardless of $\mathrm{\Delta }T$. The error bars are S.D. from the five to 10 sets of the image data. These results suggest that the origin of the rippling is capillary waves.

Figure 7

Enhanced vaporization by rippling. (a) Schematic of vapor diffusion from a vapor disk region into a rippling region. (b) $V$ (the total vapor volume between the liquid drop and the substrate) measured (open circle) from the x-ray snapshots and estimated based on Eq. (6) (dashed line) assuming continuous growth of the vapor disk without rippling, as a function of time for different $T_s$. After rippling time $\left(t_r\right)$, the measured volume is getting bigger than estimated. The difference gets larger at higher $T_s$.

Figure 8

Growth of vapor disks for various liquids. (a)–(b) Vapor disk thickness vs $t^{0.5}$ in different $T_s$ for (a) isopropanol and (b) methanol drops, consistently showing linear growth with $t^{0.5}$ regardless of temperature. Dashed lines are the best linear fittings of the data. The error bars are S.D. from the five to 10 sets of image data. (c) Vapor disk thickness normalized by $t^{0.5}\mathrm{v}\mathrm{s}\mathrm{\Delta }{T}^{0.5}$ for different liquids. α is the slope of $\delta /t^{0.5}\mathrm{v}\mathrm{s}\mathrm{\Delta }{T}^{0.5}$. (d) α vs $L$ (latent heat of the liquid drop); the red solid line is the best fit for the three liquids with allometric scaling: $\alpha \propto L^{-0.42}$. By extrapolating to water drop ($L$ ∼2260 J/g; red diamond), the α value for water is estimated as $2.9\times {10}^{-5}\mathrm{m}/{\mathrm{s}}^{0.5}/{\mathrm{K}}^{0.5}$