Self-propelled Leidenfrost droplets on femtosecond-laser-induced surface with periodic hydrophobicity gradient

The controllable transfer of droplets on the surface of objects has a wide application prospect in the fields of microfluidic devices, fog collection and so on. The Leidenfrost effect can be utilized to significantly reduce motion resistance. However, the use of 3D structures limits the widespread application of self-propulsion based on Leidenfrost droplets in microelectromechanical system. To manipulate Leidenfrost droplets, it is necessary to create 2D or quasi-2D geometries. In this study, femtosecond laser is applied to fabricate a surface with periodic hydrophobicity gradient (SPHG), enabling directional self-propulsion of Leidenfrost droplets. Flow field analysis within the Leidenfrost droplets reveals that the vapor layer between the droplets and the hot surface can be modulated by the SPHG, resulting in directional propulsion of the inner gas. The viscous force between the gas and liquid then drives the droplet to move.


Introduction
The directional and spontaneous transfer of droplets on the surface of objects has wide applications [1][2][3] in fog collection and water transportation [4,5], drug delivery and mixing [6], microfluidic devices [7][8][9][10], and heat transfer technologies [10].The philosophy underlying such propulsion is to generate asymmetric force on droplets, which can be realized Original content from this work may be used under the terms of the Creative Commons Attribution 4.0 licence.Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. by anisotropic surface topography [4,[11][12][13][14][15] and the gradients of light [16], temperature [17,18], and electrical force [19][20][21].Although these methods can provide enough driving force, there is usually a large solid-liquid interface, which will dramatically enhance the resistance force [22][23][24].Therefore, much energy should be devoted to propelling the droplets.The Leidenfrost effect can be introduced to overcome such a limitation [25][26][27][28].
Because of the vapor layer resulted from the Leidenfrost effect, the droplets will hover over the surface and have no physical contact with the surface, which can eliminate the friction resistance.If a droplet is in Leidenfrost state, a preferential self-propulsion will take place when asymmetric structures are introduced [29][30][31][32].Among them, the ratchet structures are most widely studied, which allow directional propulsion of droplets over long distances.However, the 3D structures restrict their broad application in microelectromechanical system-based fluidic devices, which are normally based on thin silicon or glass substrates.Thus, it is required to prepare 2D or quasi-2D geometry to manipulate the droplets.
Different from the Janus-textured substrates [33] and the planar ratchets [34], we propose to apply spatially-varyingwettability to realize the directional propulsion.It is of note that the wettability of the surface was found to deeply affect the Leidenfrost effect.Vakarelski et al showed that the superhydrophobic surfaces can stabilize the Leidenfrost vapor layer [26].And compared to the superhydrophobic surface, the hydrophilic surface can increase the Leidenfrost point significantly [27,35], which is the temperature boundary between the transition and film boiling regimes.Therefore, controlling the wettability is a potential approach to achieve Leidenfrost droplet manipulation.However, previous studies mainly focused on the influence of two types of wettability, hydrophilic and superhydrophobic.It is not clear whether the continuous change of the wettability will have different effects on the Leidenfrost effect.Therefore, the surface with periodic hydrophobicity gradient (SPHG) is required to verify the conjecture.
Femtosecond laser is an ideal method to fabricate the surfaces with special wettability.On one hand, it is easy to process various micro-nano structures to obtain different wettability [36].On the other hand, the selective processing capability of laser can realize wettability control in different areas.Compared to processing methods such as photolithography and plasma etching, femtosecond laser processing has lower costs, a simpler preparation process, better mechanical stability, and less secondary pollution [37][38][39].Furthermore, due to the nonlinear effects of femtosecond lasers and the smaller heat-affected zone, femtosecond laser processing of surface micro-nanostructures produces less burrs or debris as same as the case of nanosecond laser ablation [40].
Herein, femtosecond laser is applied to fabricate a SPHG, based on which we realize the directional self-propulsion of the Leidenfrost droplets.It provides a new method to control the Leidenfrost droplets.Four types of micro-nano structures induced by femtosecond laser, which have different hydrophobicity, show different influences on the Leidenfrost effect.Based on the above phenomenon, the droplets move directionally on the SPHG.The flow fields inside Leidenfrost droplets indicate that the vapor layer between Leidenfrost droplets and hot surface can be modulated by the SPHG, which results in the directional propulsion of the inner gas.Then, the viscous force between gas and liquid drives the ball to move.

Fabrication of SPHG
Figure 1 illustrates the fabrication process of the SPHG and a schematic diagram of a self-propelled Leidenfrost droplet.The SPHG is fabricated on a silicon wafer using shaped femtosecond laser and subsequent chemical treatment (see Methods), as shown in figure 1(a).Each hydrophobicity period is divided into four regions with distinct micro-nano structures which are controlled by regulating the fluence of the femtosecond laser.Modulating the femtosecond laser into a rectangle significantly improves fabrication efficiency compared to direct laser writing.The SPHG is then heated by a hot plate.
At a certain temperature, water droplets exhibit preferential propulsion from superhydrophobic to hydrophobic areas, as shown in figure 1(b).We will discuss the details of this work, focusing on the influence of the surface with different micro/nanostructures on the Leidenfrost effect.
Nanoscale particles cover the surface due to Coulomb explosion during femtosecond laser ablation, allowing for easy fabrication of hierarchical structures without complex lithography procedures [41,42].Figure 2(a) displays topographies under different femtosecond laser power and corresponding magnified images.The micro/nanostructure topographies differ significantly: (1) without femtosecond laser processing, the surface is the original polished surface with low roughness; (2) under low laser power of 0.3 mW, near the silicon ablation threshold, a Laser-Induced Periodic Surface Structure is processed with an average depth of 150 nm and period of approximately 600 nm, resulting in higher roughness than the original surface; (3) as laser power increases, discrete granular structures form with increasing depth and roughness at higher power levels.The results from the laser confocal microscope show that the greater the laser energy is, the greater the roughness of the processed silicon surface (figure S7).These results indicate that adjusting the laser fluence can precisely control the surface topographies.

Hydrophobicity control and the influence on the Leidenfrost effect
After chemical treatment, we measured the contact angles of surfaces fabricated at different laser powers (figures 2(a) and (b)).There is a strong dependence of contact angle on laser power.When laser power is below 2 mW, contact angle increases with increasing laser power.The unprocessed surface has the smallest contact angle of 112 • while the largest contact angle of 157 • is achieved at a laser power of 2 mW.However, considering the impact of measurement errors, further increases in laser power result in little change in contact angle.These results indicate that varying hydrophobicity can be achieved on silicon surfaces by using femtosecond lasers at different powers.Thus, femtosecond lasers provide an ideal tool for SPHG fabrication.To create a hydrophobicity gradient on SPHG, we selected four regions with original topography and topographies induced by laser powers of 0.3 mW, 0.6 mW and 2 mW to make up a hydrophobicity period.As shown in figure 2(b), these regions have contact angles of 112 • , 141 • , 151 • and 157 • respectively.This result shows that as the surface roughness increases, the contact angle also increases, which is consistent with the Wenzel model.It should be noted that using higher power lasers for surface treatment often produces more debris, which may affect other areas treated with lower energy.Therefore, to ensure consistent contact angles,  we choose to use lower laser energy for surface treatment of materials.
To investigate the influence of varying hydrophobicity on the Leidenfrost effect, we compared the state changes of water droplets (with a volume of approximately 6 µl) after being dropped onto surfaces with four different levels of hydrophobicity.Figure 3 illustrates the motion states of water droplets at temperatures ranging from 100 • C to 180 • C. As the temperature increases, the vertical motion of the droplet is significantly affected by the Leidenfrost effect.For ease of description, we have divided the vertical motion state into four categories: (I) Fixation: at temperatures below the Leidenfrost point, no vapor cushion is formed, resulting in a high viscous force between the surface and droplet.Consequently, the droplet remains fixed on the surface without any solid-liquid separation.
(II) Bouncing one to three times: when the temperature is near the Leidenfrost point, a thin vapor cushion reduces the viscous force, causing the droplet to bounce upon impact with the surface.However, due to residual viscous force, bouncing ceases after one to three repetitions.(III) Bouncing four to six times: at higher temperatures, viscous force is further reduced and the number of bounces increases to four to six.(IV) Continuous bouncing: at even higher temperatures, droplets levitate completely on a vapor cushion.Viscous force becomes negligible and droplets bounce continuously for a period of time.
As shown in figure 3, there are distinct differences in vertical motion changes on each of the four surfaces: (1) When dropped onto an unprocessed surface, droplets remain fixed at temperatures ranging from 100 • C to 160 • C before transitioning to continuous bouncing at These results indicate that as temperature increases, all droplets eventually transition into continuous bouncing.Therefore, critical temperatures for continuous bouncing can be used to compare Leidenfrost points.Critical temperatures for surfaces processed by 0 mW, 0.3 mW, 0.6 mW and 2 mW femtosecond lasers are 180 • C, 160 • C, 140 • C and 120 • C respectively.Thus, as hydrophobicity decreases, Leidenfrost points increase.This suggests that femtosecond lasers can be used to control surface hydrophobicity and thereby manipulate Leidenfrost effects.Combined with femtosecond laser's spatio-selective fabrication capability, SPHG can be easily obtained for manipulating Leidenfrost droplets.

Droplets self-propelled by Leidenfrost on the SPHG
In this study, we investigated the hydrophobicity gradient period of the SPHG, which was found to be 500 µm.The widths of the regions processed by 0 mW, 0.3 mW, 0.6 mW, and 2 mW, lasers were determined to be 50 µm, 80 µm, 70 µm, and 300 µm, respectively.Although the Leidenfrost points on these four regions were nearly linear, the forces acting on the Leidenfrost droplets were not necessarily linear.As such, the ratio of these four regions was obtained through several experiments.It should be noted that the maximum depth of laserinduced surface structures is only a few micrometers, which is negligible compared to the hydrophobicity gradient period of the SPHG.Therefore, the SPHG structure proposed in this paper can be considered a 2D structure rather than a 3D structure (figure S8).
It is worth noting that the resistance experienced by Leidenfrost droplets is minimal.As a result, even a small force component of gravity caused by the tilt of the sample can cause droplet movement.To eliminate this influence, two structures with opposite hydrophobicity gradient directions were processed on a single silicon wafer (figure 4(a)).When the sample was heated to 150 • C and a 6 µl water droplet was gently dropped from a height of 3.7 mm, it was rectified into a preferential direction along the direction from superhydrophobic to hydrophobic areas.Furthermore, the direction of droplet movement on these two structures was opposite and remained unchanged when the sample was rotated by 90 • (figure 4(a)).This indicates that preferential propulsion is not due to sample tilt; otherwise, droplets would move in the same direction on both structures.High-speed imaging was used to visualize the movement of Leidenfrost droplets.Figure 4(b) shows four snapshots of droplet's position with a red dotted line indicating the trajectory of the droplet's center.In addition to preferential movement, droplets also exhibited bouncing behavior.Figure 4(c) shows the evolution of the droplet velocity on SPHG over time.Upon contact with substrates, Leidenfrost droplets accelerated and eventually reached a steady velocity.The SPHG resulted in an acceleration and steady velocity of 80 mm s −2 and 20 mm s −1 , respectively.Notably, droplet's steady velocity on SPHG was comparable to that on traditional ratchets.
The self-propelled process of Leidenfrost droplet on the SPHG shows strong sensitivity to temperature.As shown in figure 5, self-propulsion did not occur below 130 • C due to high viscous forces between droplets and the surface that prevented movement (figure 3).As the temperature increased from 130 • C, maximum velocities of Leidenfrost droplets gradually increased (figures 5(a) and (b)).This increase in velocity can be attributed to increasing vapor thickness with temperature, resulting in reduced viscous force (figure 5(c)).Acceleration also increased with temperature, providing further evidence for decreasing viscous force.
In addition to temperature, we further studied the impact of volume and drop height of droplets on self-propulsion.Three types of needles with different diameters were used to control volume, and droplets with volumes of 5.6 µl, 8.2 µl and 11.5 µl were dropped onto the surface.As shown in figure S5, the maximum velocities of Leidenfrost droplets were found to be nearly identical regardless of volume.On the other hand, maximum velocities decreased gradually as drop height increased (figures 6(a) and (b)).Compared to a drop height of 2.3 mm, maximum velocity decreased by about 10 mm s −1 when dropped from a height of 5.1 mm.
To explain this decrease in maximum velocity with increasing drop height, we used high-speed cameras to record droplet trajectories.As shown in figure 6(c), after moving for some time, bounce height stabilized and was positively correlated with drop height.This suggests that contact time between droplets and the surface is negatively correlated with drop height.Since vapor cushion influence on droplets is a driving force for movement, longer contact times result in higher maximum velocities and vice versa.
According to the trajectory of glass microspheres, it can be seen that at the temperature of 160 • C, the fluid inside the Leidenfrost droplet on SPHG surfaces exhibits obvious directional rotational motion (figure 7(a), videos 4-6).In contrast, when the droplet is on a uniform superhydrophobic surface, the glass microspheres inside the Leidenfrost droplet do not exhibit the same directional rotational motion.This result indicates that the internal flow of the droplet on a uniform superhydrophobic surface is essentially stationary (video 7).It is worth noting that on SPHG surfaces, the direction of fluid motion on the contact surface of solid and liquid is consistent with the directional motion of the droplet.According to the Leidenfrost effect, the vapor layer separates the droplet from the solid surface, and the friction generated by the relative motion between the vapor layer and the droplet acts as the driving force for the directional rotational motion inside the droplet.According to the direction of flow field motion on the solid-liquid contact surface, it can be inferred that at this time, the direction of gas motion in the vapor layer is consistent with the direction of droplet motion, that is, gas moves directionally  from areas with stronger hydrophobicity to areas with weaker hydrophobicity (figure 7(b)).From the previous results, it can be known that, on SPHG surfaces, each region has a different Leidenfrost state at the same temperature.Gas film thickness in poorly hydrophobic areas is thinner than that in strongly hydrophobic areas, resulting in greater heat transfer between solid and liquid and faster gas dissipation rates.In contrast, gas dissipation rates are slower in strongly hydrophobic areas, causing gas to flow towards poorly hydrophobic areas and form directional air flow that drives droplet movement.

Conclusion
Herein, femtosecond laser is applied to fabricate a SPHG, based on which we realize the directional self-propulsion of the Leidenfrost droplets.Four types of micro/nanostructures induced by femtosecond laser, which have different hydrophobicity, show different influences on the Leidenfrost effect.Based on the above phenomenon, the droplets move directionally on the SPHG.The flow fields inside Leidenfrost droplets indicate that the vapor layer between Leidenfrost droplets and the hot surface can be modulated by the SPHG, which results in the directional propulsion of the inner gas.Then, the viscous force between gas and liquid drives the ball to move.This work provides a brand-new method for controlling the movement of droplets and expands the scope of application.

Materials and fabrication:
A Gaussian femtosecond laser (Spitfire Ace, Spectra-Physics, USA) with 35 fs pulse duration, 800 nm wavelength and 1 kHz repetition rate were used to perform the experiment.The samples were hydrophobized by silanization with a silane reagent ((Trichloro (1 H, 1 H, 2 H, 2 H perfluorooctyl) silane, 97% Aldrich)), which can decrease the surface energy and achieve hydrophobicity.To improve the silane deposition, the samples were pre-treated using the plasma-cleaning device.The sample was then placed in a confined space together with an open petri dish with several drops of the reagent.The confined space is evacuated to low vacuum for about half an hour to carry out the vapor phase deposition of the agent on the sphere surface.The coating is stable upon heating to about 220 • C.
Instruments and characterization: a high-speed camera at a framerate of 700 frames s −1 was used to take the side-view images of the droplets.An industrial microscope (BX53, OLYMPUS, Japan) was used to obtain the optical microscope images.

Figure 1 .
Figure 1.SPHG processing and application diagram.(a) The schematic diagram of the SPHG fabrication by femtosecond laser direct writing.The inserts show the confocal laser scanning microscope (CLSM) results of the four types of topography induced by femtosecond laser.(b) The schematic diagram of a self-propelled Leidenfrost droplet on SPHG.

Figure 2 .
Figure 2. Influence of different surface morphology on droplet contact angle.(a) The evolution of micro/nanostructures topography with the increase of femtosecond laser energy and the corresponding contact angles.The SEM pictures in the middle row and bottom share the same scale bar, respectively.The contact angles on different surfaces were observed at room temperature.(b) The contact angles of the surface under different femtosecond laser power after chemical treatment.The laser power corresponding to the four points marked by a red dotted line is used to fabricate the SPHG.

Figure 3 .
Figure 3.The motion states of water droplets at different temperatures from 100 • C to 180 • C (video 1).

Figure 4 .
Figure 4. Droplet self-drive process on SPHG.(a) The schematic diagram of two structures with opposite hydrophobicity gradient direction and the preferential propulsion of the Leidenfrost droplets in different directions (video 2).(b) The snapshots of the preferential propulsion of Leidenfrost droplets and the trajectory of the center of the droplet.(c) The change of droplet velocity at Leidenfrost state with time on the SPHG.These experimental results were obtained at a temperature of 150 • C.

Figure 5 .
Figure 5. Influence of different heating temperatures on droplet self-driving process.(a) Selected snapshots showing the displacement at different temperatures.(b) The evolution function of the Max velocity as temperature.(c) The change of droplet velocity at Leidenfrost state with time at different temperatures.

Figure 6 .
Figure 6.Influence of different falling heights and droplet volumes on self-driven process.(a) The evolution function of the Max velocity as drop height.(b) Time evolution of droplet moving velocity from different drop heights.(c) The trajectory of the center of the droplet dropped from the heights of 2.3 mm and 5.8 mm (video 3).

Figure 7 .
Figure 7.The directional rotational motion of Leidenfrost droplet on SPHG surfaces.(a) The snapshots of the flow field inside Leidenfrost droplets.(b) The schematic diagram of the friction and air layer flow (videos S4-6).