Droplet｜无预设通道下液滴的可编程曲线自推进

Shile Feng^1,2, Yongping Hou¹, Yongmei Zheng¹

(¹Key Laboratory of Bio-inspired Smart Interfacial Science and Technology of Ministry of Education, Institution of Chemistry, Beihang University (BUAA), Beijing, China; ²State Key Laboratory of High-performance Precision Manufacturing, Dalian University of Technology, Dalian, China)

Curvilinear self-propelling of droplets has attracted great interest in the past few decades due to their irreplaceable roles in many areas. Conventional understanding is that a droplet moves only along a preset channel formed by morphology or chemical components. Achieving programmable curvilinear droplet motion independent of a preset channel remains greatly challenging. Here, we report a programmable curvilinear self-propelling of droplets (circle, divergence, and convergence) based on the collaboration of the curvilinear wetting gradient and the Leidenfrost effect. This design achieves motion trajectory in a well-controlled manner as well as high velocity and long distance of droplet transport independent of the preset channel. Moreover, the motion behaviors of droplets could be predicted accurately by theoretic simulation. We envision that our unique design could manifest extensive practical applications in fluidic devices, liquid transport, and heat transfer systems.

Fig.1 Design concept of a surface with circle wetting gradient for controlled circle self-propelling of the droplet. (a) Apparatus and schematic diagrams of the formation of circle wetting gradient (CWG) on graphite plate. In the anodizing process, oxygen-containing groups including hydroxy, carbonyl, and carboxyl are formed during the continuous oxidation of reactive carbon atoms to adjust the surface wetting property. We control the electrolyte level parallel with the center of the circular graphite plate and clockwise rotate the graphite plate for half a cycle to form a circle gradient of oxygen-containing group content as well as a circle wetting gradient. The color changes from blue to red mean that the wetting performance changes from hydrophobic to hydrophilic, which applies to all figures in our article. (b) Directional spreading of the droplet on the CWG along the wetting gradient. The circle wetting gradient can induce contact angle difference at the front and rear side of a droplet (β₂ < β₁) and forms a direction-changed total driving force (F_T) during the spreading process to realize the circle spreading of a droplet. (c) The long-range circle was the self-propelling of a droplet at high temperature. The wetting gradient can induce a thickness gradient of vapor cushion at the front and rear sides of the droplet (h₂ < h₁), which forms a driving force to transport the droplet along the wetting gradient with a long range and high speed.

Fig.2 The manifestation of the water contact angle (CA), wetting gradient line, and droplet self-propelling behavior on the designed CWG. (a) Values of CA on the designed surface via theoretical simulations and actual measurements (five-pointed star). Most of the measured points are present on the simulation CA surface. (b) Simulations of the wetting gradient line. It is clear to see that the wetting gradient lines (white lines) are a series of concentric semicircles. P is the coordinates of the measuring point in the x and y directions. (c) The value of the O/C ratio on the graphite plate treated by different oxidation times. The ratio of O/C increases from 2.5% to 19.8% gradually with the increase of oxidation time. (d) Change of CA versus polar angle θ with different total reaction time T (ρ = 10 mm). For T < 40 s, the value of the wetting gradient increases with the increase of T. For T > 40 s, the linear relationship between the water contact angle and polar angle disappears. (e) Circle the self-propelling of droplets on the designed droplet actuator at 150°C with different initial positions. e1, at point of (ρ, θ) = (10, 2°). e2, at point of (ρ, θ) = (8, 2°). The dotted lines and arrows express the wetting gradient line at the initial dripping point and the self-propelling direction of the droplet, respectively. The volume of the droplet is 8 µL, and the scale bar is 5 mm. t is the time the droplet takes to pass a corresponding distance in the figures.

Fig.3 Illustration for the mechanism of circle self-propelling of a droplet on a designed circle actuator at high temperature. (a) Relationship of vapor cushion thickness (h) with the contact angle (CA). There seems to be a linear relationship: h = −78.6 + 3.0 CA. (b) A gradual decrease in the thickness of the vapor cushion along the wetting gradient induces a driving force to actuate droplets along the wetting gradient line. (c) Change in the thickness of the vapor cushion along the droplet self-propelling trajectory. (d) Force analysis of droplet sitting on the vapor cushion with a thickness gradient (tilted angle of α). Three forces are exerted on droplets, for example, gravity force mg, vapor propelling force F_V, and friction force F_f. Here, F_p is the resultant force of F_V and the gravity force. (e) Plots of experimental and simulated results about the relationship between S and t on trajectories with r of 8 and 10 mm. The experimental, simulated, and predicted results are highly consistent, which indicate that the theoretical model is valid. (f) Predicted self-propelling distance of droplet at any given values of r and t.

Fig.4 Curvilinear self-propelling of a droplet on the designed surfaces with divergence and convergence wetting gradients at 150°C. (a, b) Schematic diagram of the region division on surfaces with divergence (L < 0) and convergence wetting gradients (L > 0). α₁ is the geometrical angle between the horizontal line and radius O2. L is the relative position between the liquid level and the circle center. (c, d) Theoretical simulation of the wetting gradient line on surfaces with divergence and convergence wetting gradients. (e, f) Curvilinear self-propelling of a droplet on the designed surfaces at 150°C. On the designed surface with divergence wetting gradient at points of (8, 15°) (e1) and (4, 15°) (e2), the droplet deviates from the center gradually and finally detaches from the edge. On the designed convergence wetting gradient at points of (12, 30°) (f1) and (10, 90°) (f2), the droplet performs to move partially to the center gradually and then converges to region III (wetting area). (g) Simulation of the wetting gradient configuration of surfaces designed with L = 0, ±4.5, ±6 mm, and corresponding curvilinear self-propelling of droplets at 150°C. It is clear to see that the droplet exhibits different self-propelling trajectories on surfaces even though the initial positions are similar to each other. The dotted line and arrow express the wetting gradient line and self-propelling direction of the droplet. The volume of the droplet is 8 µL, and the scale bars are 5 mm. CA, water contact angle.