Self-Propulsion of Boiling Droplets on Thin Heated Oil Films

We report on the self-propulsion of boiling droplets which, despite their contact with viscous, immiscible oil films, attain high velocities comparable to those of levitating Leidenfrost droplets. Experiments and model reveal that droplet propulsion originates from a coupling between seemingly disparate short and long timescale phenomena due to microsecond fluctuations induced by boiling events at the droplet-oil interface. This interplay of phenomena leads to continuous asymmetric vapor release and momentum transfer for high droplet velocities.

Figure 1

(a) A sequence of images of a water droplet on an untextured, plain silicon surface at 180 °C. The drop first boils then bounces in the Leidenfrost state, moving slowly to the right under the influence of gravity. (b) A water droplet self-propelling on a silicon surface coated with a thin, 13 m Pas silicone oil film at 180 °C. (c) Self-propelling droplet (blue triangles) and Leidenfrost droplet (black squares) position as a function of time for a droplet on a 16 m Pas silicone oil film at 160 °C. Self-propulsion velocities, calculated using the slope of the red line, are constant after droplets heat and accelerate.

Figure 2

The images below each schematic show frames from a high-speed video of a self-propelling droplet ejecting a bubble on a 130 m Pas oil film at 180 °C. (a) Heat transfer from the heated oil film to the droplet drives the evaporation of the droplet. (b) A bubble grows and is ejected, propelling the droplet to the right. The dashed red line denotes the outline of an ejecting bubble. (c) Filaments form due to shear stripping during vapor ejection. Momentum ejection is balanced by the viscous shear force at the circumference of the droplet’s base. (d) Droplet velocity is independent of droplet radius, as predicted by the scaling model. The dashed black line denotes the average velocity of $50\mathrm{mm}/\mathrm{s}$. Experiments were conducted on 19 m Pas oil films at 140 °C. Horizontal error bars denote the range of droplet radii included in each point. Vertical error bars correspond to the standard deviations. (e) Droplet velocities as a function of oil viscosities at 140 °C, 160 °C, and 180 °C for flat and textured surfaces (see Methods in Supplemental Material [23]). Droplet velocities are not significantly affected by surface texture. The solid black and dashed red line fits correspond to $U=8.5{\mu }^{-5/8}$ and $U=2.3{\mu }^{-1}$, respectively. Reported velocities are the average of 3–6 self-propulsion events.

Figure 3

The proposed model and experimental evidence suggest that the droplet velocity is a result of boiling phenomena occurring on two significantly different timescales. (a) Bubble ejections occurring at millisecond timescales result in the overall momentum ejection and propulsion velocities (Supplemental Material, Video 6 [23]). The images are of a droplet propelling from left to right on a 13 m Pas silicone oil film at 180 °C. (b)–(d) Evidence of boiling events occurring on the $10\mu \mathrm{s}$ timescale under the droplet that can affect the thermal and momentum boundary layers in the oil film, producing the $U\sim {\mu }^{-5/8}$ observed in Fig. 2 and explained by the model. Full high-speed videos are included as Video 5 in Supplemental Material [23]. (b),(c) Spatiotemporal diagrams on the right are created using the line of pixels on the dot-dashed red lines on the images on the left. (b) Self-propelling droplet demonstrating rapid surface fluctuations. Videos were taken on a 19 m Pas oil film at 140 °C between vapor ejection events. (c) In contrast, a Leidenfrost droplet has no notable surface fluctuations. (d) Normalized image intensity over time along the dashed lines in the spatiotemporal diagrams. The timescale of the fluctuations is on the order of $10\mu \mathrm{s}$.

Figure 4

Dimensionless velocity plotted against the dimensionless parameter predicted by the scaling law in Eq. ((9)). Experiments, which vary viscosity from 10 to 200 m Pas, temperature from 140 °C to 180 °C, and surface texture, collapse onto a line with slope 0.9 and $R^2=0.87$. Reported velocities are the average of 3–6 self-propulsion events, and error bars correspond to standard deviations.