Modeling drag reduction and meniscus stability of superhydrophobic surfaces comprised of random roughness

Abstract

Previous studies dedicated to modeling drag reduction and stability of the air-water interface on superhydrophobic surfaces were conducted for microfabricated coatings produced by placing hydrophobic microposts/microridges arranged on a flat surface in aligned or staggered configurations. In this paper, we model the performance of superhydrophobic surfaces comprised of randomly distributed roughness ͑e.g., particles or microposts͒ that resembles natural superhydrophobic surfaces, or those produced via random deposition of hydrophobic particles. Such fabrication method is far less expensive than microfabrication, making the technology more practical for large submerged bodies such as submarines and ships. The present numerical simulations are aimed at improving our understanding of the drag reduction effect and the stability of the air-water interface in terms of the microstructure parameters. For comparison and validation, we have also simulated the flow over superhydrophobic surfaces made up of aligned or staggered microposts for channel flows as well as streamwise or spanwise ridges configurations for pipe flows. The present results are compared with theoretical and experimental studies reported in the literature. In particular, our simulation results are compared with work of Sbragaglia and Prosperetti, and good agreement has been observed for gas fractions up to about 0.9. The numerical simulations indicate that the random distribution of surface roughness has a favorable effect on drag reduction, as long as the gas fraction is kept the same. This effect peaks at about 30% as the gas fraction increases to 0.98. The stability of the meniscus, however, is strongly influenced by the average spacing between the roughness peaks, which needs to be carefully examined before a surface can be recommended for fabrication. It was found that at a given maximum allowable pressure, surfaces with random post distribution produce less drag reduction than those made up of staggered posts.

Polymeric Slippery Coatings: Nature and Applications

“…Several studies have demonstrated the effect of gas fraction on the slip length [5,6,52,[79][80][81][82][83][84][85][86][87][88]. For laminar flow, slip length increases with gas fraction (Figure 22) and hence from Equation (1), velocity gradient decreases (i.e., less drag).…”

“…The figure includes both experimental and numerical results for a microchannel with a microridged superhydrophobic wall. Samaha et al [79] simulated the performance of superhydrophobic surfaces having idealized random roughness (posts or particles) and compared their results with those of surfaces with staggered posts. Their numerical simulations indicated that the gas fraction has a significant impact on the characteristics of a superhydrophobic surface, as it affects the slip length and therefore the skin-friction coefficient.…”

“…Samaha et al [79] utilized a Voronoi diagram [94] to determine the local gas fraction and the maximum pitch for superhydrophobic surfaces made up of randomly distributed posts. This information was used in Equation (2) to determine the maximum allowable hydrostatic pressure, which corresponds to the post that has the maximum local gas fraction.…”

Superhydrophobic drag reduction in laminar flows: a critical review

“…Samaha et al (2011) showed that randomly arranged posts render a slightly more slippage than regularly arranged posts of the same solid fraction. However, the random posts exhibited lower stability against the wetting transition, leading to the smaller slip lengths at a given liquid pressure.…”

“…Although it is difficult to quantify, several recent theoretical and numerical works have investigated a slip length on irregularly patterned structures (Feuillebois et al 2009;Vinogradova and Belyaev 2011;Samaha et al 2011;Cottin-Bizonne et al 2012). Samaha et al (2011) showed that randomly arranged posts render a slightly more slippage than regularly arranged posts of the same solid fraction.…”