Directional spreading of a viscous droplet on a conical fibre

Abstract

If a droplet is placed on a substrate with a conical shape it spontaneously starts to spread in the direction of a growing fibre radius. We describe this capillary spreading dynamics by developing a lubrication approximation on a cone and by the perturbation method of matched asymptotic expansions. Our results show that the droplet appears to adopt a quasi-static shape and the predictions of the droplet shape and spreading velocity from the two mathematical models are in excellent agreement for a wide range of slip lengths, cone angles and equilibrium contact angles. At the contact line regions, a large pressure gradient is generated by the mismatch between the equilibrium contact angle and the apparent contact angle that maintains the viscous flow. It is the conical shape of the substrate that breaks the front/rear droplet symmetry in terms of the apparent contact angle, which is larger at the thicker part of the cone than that at its thinner part. Consequently, the droplet is predicted to move from the cone tip to its base, consistent with experimental observations.

References in corpus (5)

• Condensation on Slippery Asymmetric Bumps
• Making a splash with water repellency
• A variational approach to the moving contact line hydrodynamics
• Hydrodynamic theory of de-wetting
• Asymptotic theory for a moving droplet driven by a wettability gradient

Cited by in corpus (5)

• Effective boundary conditions for dynamic contact angle hysteresis on chemically inhomogeneous surfaces
• Film coating by directional droplet spreading on fibers
• Sliding, vibrating and swinging droplets on an oscillating fibre
• Self-propulsion dynamics of small droplets on general surfaces with curvature gradient
• Long-distance Liquid Transport Along Fibers Arising From Plateau-Rayleigh Instability