Superhydrophobicity: Localized Parameters And Gradient Surfaces

TL;DR: In this article, the authors consider the case of a variation in Cassie-Baxter fraction across a surfac e possessing a homogeneous hydrophobic surface chemistry and discuss the conditions (droplet volume, surface hydrophobicity, gradient in superhydrophobi city and contact angle hysteresis) under which a dr oplet may be set into motion.

Abstract: The use of Cassie and Baxter’s equation and that of Wenzel have been subject to some criticism of late . It has been suggested that researchers use these equations without always considering the assumptions that ha ve been made and sometimes apply them to cases that are not suitable. This debate has prompted a reconsideration of the derivation of these equation s using the concept of parameters for the Wenzel ro ughness and Cassie-Baxter solid surface fractions that are local to the three-phase contact lines. In such cir cumstances, we show the roughness and Cassie-Baxter solid fract ions depend not only on the substrate material, but also on which part of the substrate is being sampled by the three-phase contact lines of a given droplet. W e show that this is not simply a theoretical debate, but i s one which has direct consequences for experiments on surfaces where the roughness or spatial pattern var ies across the surface. We use the approach to deri ve formulae for the contact angle observed on a double length scale surface under the assumption that the smallscale features on the peaks of larger scale feature s are either wetted or non-wetted. We also discuss the case of curved and re-entrant surface features and how t hese bring the Young’s law contact angle into the f ormula for roughness and the condition for suspending drop lets without penetration into the surface. To illus trate the use of local parameters, we consider the case of a variation in Cassie-Baxter fraction across a surfac e possessing a homogeneous hydrophobic surface chemistry and discuss the conditions (droplet volume, surface hydrophobicity, gradient in superhydrophobi city and contact angle hysteresis) under which a dr oplet may be set into motion. We show that different con tact angles on each side of a droplet of water plac ed on such a surface can generate sufficient lateral forc e for the droplet to move towards the region of the surface with the lowest contact angle. Using an electrodepo sited copper surface with a radial gradient in superhydrophobicity we exemplify these ideas by showing experimentally that droplets enter into selfactuated motion and accumulate in the centre of the surface where the wettability is higher. In princi ple, paths can be defined and water droplets can be collected by creating such gradients in superhydrophobicity t hrough changes in the lateral topography of the surface.