Abstract
This study deals with the control of the movement of liquid droplets rolling down an inclined plate based on the differences in the wettability of the plate. We used a photoreactive polymer poly(7-methacryloyloxy coumarin) (PMC) whose molecular structure can be changed reversibly to realize different wettabilities by ultraviolet irradiation. We proposed employing sawtooth patterns at boundaries between areas with different contact angles to control the droplet trajectory. Furthermore, we experimentally observed that the droplet moves along a line inclined to the direction of gravity. The droplet behavior can be analyzed using a theoretical model based on the droplet dynamics wherein the surface tension acting on the contact line and the gravitational force are considered. The theoretical results suggest that inclination from the gravitational direction can be increased if the advancing contact angle is reduced. In the experiments conducted herein, ultrasonic vibration was applied to the inclined plate to reduce the contact angle hysteresis. The results showed that the advancing contact angle actually decreased and that the droplet trajectory was controlled to realize motion along a line with inclination angle almost twice of that realized without vibration.
Graphical abstract
A saw-tooth pattern of boundary between the areas with different contact angles was proposed to control the trajectory of a droplet rolling down on an inclined plate. As shown in the right figure, the droplet immediately diverges from the direction of gravity and moves in accordance with the target lines.
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Abbreviations
- B :
-
Maximum width of a droplet [m]
- F :
-
Vector of the force applied to a droplet [N]
- g :
-
Gravitational acceleration [m/s2]
- m :
-
Ratio of straight part of contact line to the radius of the arc-like contact line [-]
- R :
-
Radius of arc-like contact line [m]
- V :
-
Liquid volume [m3]
- x :
-
Coordinate on the plate surface in the direction of gravity [m]
- y :
-
Coordinate on the plate surface in transverse direction [m]
- α (= 45°):
-
Oblique angle of the UV-irradiated area in Pattern A [°]
- β :
-
Inclination angle of moving droplet [°]
- δ :
-
Variation in the contact angle [°]
- η :
-
Center angle of the arc-like contact line (advancing side, ref. Fig. 4) [°]
- θ :
-
Contact angle [°]
- µ :
-
Target inclination angle of droplet movement [°]
- ρ :
-
Liquid density [kg/m3]
- σ :
-
Surface tension [N/m]
- φ :
-
Inclination angle of the test plate [°]
- ψ :
-
Center angle of the arc giving the receding contact angle (receding side, ref. Fig. 4) [°]
- ′:
-
UV-irradiated
- A :
-
Advancing
- R :
-
Receding
- x :
-
Gravity direction on the plate surface
- y :
-
Transverse direction on the plate surface
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Acknowledgements
A part of this research was supported by Japan Society for the Promotion of Science (JSPS) Grant Number 15K05802.
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Katoh, K., Tamura, H., Sato, E. et al. Control of droplet movement on an inclined wall with sawtoothed wettability pattern by applying ultrasonic vibration. Exp Fluids 59, 141 (2018). https://doi.org/10.1007/s00348-018-2592-2
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DOI: https://doi.org/10.1007/s00348-018-2592-2