General Way To Compute the Intrinsic Contact Angle at Tubes

Nanostructured coatings of superwettability, especially at the outer and inner surfaces of large-scale tubes, have generated broad interests for anti-biofouling, drag reduction, condensation heat transfer, and so on. The contact angle, a major parameter to evaluate the wettability, is derived and gradually modified mainly for flat surfaces after Thomas Young (1773-1829). However, in the case of tubular surfaces, the curvature affects and biases the measurement. In this article, a tube-in-tube coaxial anodization approach is developed to generate coatings of nanotube arrays at the outer surface of Ti tubes. The wetting property of the resulting nanotubes is tailored; the apparent contact angle (measured in the radial plane) deviates substantially from its intrinsic value (measured in the axial plane) as the tube diameter decreases or droplet size increases. A general equation, suitable for tubular surfaces of different wetting states, is hence derived to compute the intrinsic contact angle in terms of apparent contact angle, droplet radius, and tube radius. Intrinsic contact angles calculated using the equation agree well with the values measured directly from the corresponding flat surface, validating its effectiveness. This study provides a theoretical basis to assess the wetting property of tubular or curved surfaces by eliminating the curvature effect.