Predicting shape and stability of air–water interface on superhydrophobic surfaces with randomly distributed, dissimilar posts

Abstract

A mathematical framework developed to calculate the shape of the air-water interface and predict the stability of a microfabricated superhydrophobic surface with randomly distributed posts of dissimilar diameters and heights is presented. Using the Young-Laplace equation, a second-order partial differential equation is derived and solved numerically to obtain the shape of the interface, and to predict the critical hydrostatic pressure at which the superhydrophobicity vanishes in a submersed surface. Two examples are given for demonstration of the method's capabilities and accuracy.

Identifying the Transition Capillary Pressure of a Superhydrophobic Surface Containing Cylindrical Rods

“…The standard deviation from the averaged values of ª min is roughly 2% and is included in Figure 6. Using m = 131.5 in eqs 3 and 6 gives P crit = 3322 Pa, which is roughly 2% lower than the value of 3400 Pa found by Emami et al 10 Bearing in mind that this model assumes a uniform post height and is based on the averaged values of many models, this is well within reasonable error.…”

“…The surface's macroscale properties define the conditions under which this occurs, and their prediction will allow better design of new superhydrophobic surfaces. The shape of the LV interface surrounding the circular columns and its change with capillary pressure has been modeled by Emami et al 10 Their work has also been extended to superhydrophobic surfaces made from layers of spherical particles, 5 further highlighting the similarities between this topic and the flow through porous media.…”

“…6 One of the simplest cases to consider is an array of regularly spaced vertical posts that support the LV interface and reduce the wetted solid surface area ( Figure 1A, top). Such structures have been modeled by Extrand,7,8 Zheng et al, 9 and Emami et al 10 It was found that the cross-sectional shape of the posts and their spacing are important geometric properties to take into account when designing the surface or calculating its properties. Sharp edges will pin the three-point contact (TPC), where the LV interface meets the solid surface, to the top of the post.…”

“…Emami et al 10 modeled posts in a regular square packing arrangement ( Figure 1B) with R C = 10¯m, A SL * = 0.35, and ª = 120°. It was found that at a capillary pressure of 7000 Pa, ª min approached 120°.…”

“…Emami et al 10 also expanded their square packing model to one containing randomly distributed posts with varying diameters of between 8 and 12¯m and varying heights of 50 to 51¯m, the contact angle was kept at 120°and A SL * remained at 0.35. Using this information, forty Surface Evolver models were created with randomly distributed posts in a periodic cell that had the same characteristics.…”