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Control of droplet movement on a plate with micro-wrinkle by difference of wettability


In this study, we consider the control of a liquid droplet movement rolling down on an inclined plate with gravitational force using a micro-wrinkle on a wall. The micro-wrinkle was manufactured by the buckling of a thin polymer film (poly(N-vinylcarbazole), PVK) on a base polymer (poly(vinyl chloride), PVC). The PVC was stretched once and then PVK (~ 100-nm thickness) was spin-coated on the surface of the base polymer at ambient temperature. When the strain was released in a thermostatic chamber heated above the glass transition temperature of PVC, a two-dimensional micro-wrinkle having a wavelength of several micrometers was formed on the surface. The advancing and receding contact angles were measured in directions parallel and perpendicular to the wrinkle. It was observed that there were several degrees of contact angle anisotropy. When the droplet was set on the wrinkle surface inclined at 45° to the gravitational force, the direction of droplet movement could be changed by ~ 20° from the gravitational direction. The deflection angle was estimated from a theoretical model with the principle of minimum work of the contact line.

Graphic abstract

The micro-wrinkle was manufactured by the buckling of a thin polymer film (poly(N-vinylcarbazole), PVK) on a base polymer (poly(vinyl chloride), PVC). It was observed that there were several degrees of contact angle anisotropy dependent on the direction in normal and parallel to the wrinkle. When the droplet was set on the oblique wrinkle, the direction of droplet sliding movement could be changed by ~20° from the gravitational direction in the plane as shown in the figure below. The deflection angle β can be roughly estimated from a theoretical model with the principle of minimum work of the droplet.

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E :

Energy change of droplet per unit length [J/m]

E P :

Potential energy change of droplet per unit length [J/m]

F PS :

Drag of surface tension parallel to wrinkle [N]

F VS :

Drag of surface tension perpendicular to wrinkle [N]

g :

Gravitational acceleration [m/s2]

r :

Coordinate in radial direction

Ra :

Arithmetic average roughness [m]

s :

Coordinate along contact line [m]

V :

Liquid volume [m3]

W :

Droplet width [m]

z :

Coordinate in the upward direction from top of droplet [m]

α :

Oblique angle of micro-wrinkle [°]

β :

Deflection angle of moving droplet [°]

η :

Azimuthal angle on contact line [°]

θ :

Local contact angle [°]

ρ :

Liquid density [kg/m3]

σ :

Surface tension [N/m]

φ :

Critical sliding angle of droplet [°]




Parallel to wrinkle


Perpendicular to wrinkle




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The authors are grateful to Mr. Ryohei Tanino for his effort in the experimental measurements.

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Correspondence to Kenji Katoh.

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Katoh, K., Sato, E., Yoshioka, S. et al. Control of droplet movement on a plate with micro-wrinkle by difference of wettability. Exp Fluids 60, 140 (2019).

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