Fractal Model for Wettability of Rough Surfaces

Abstract

This paper presents a fractal model to describe wettability on multiscale randomly rough surfaces. Hydrophobic or superhydrophobic surfaces, produced by processes such as electrodeposition and etching, lead to the creation of random roughness at multiple length scales on the surface. This paper considers the description of such surfaces with a fractal asperity model based on the Weierstrass-Mandelbrot (W-M) function, where the fractal parameters are uniquely determined from a power spectrum of the surface. By use of this description, a model is presented to evaluate the apparent contact angle in the different wetting regimes. The model is predictive in that it does not use any empirical or correlatory fitting of parameters to experimental data. Experimental validation of the model predictions is presented on various hydrophobic and superhydrophobic surfaces generated on several materials under different processing conditions. The contact angle is found be strongly dependent on the range of asperity length scale and weakly dependent on the fractal dimension for a surface with stable Cassie state. Based on the fractal description, desired surface roughness characteristics for generating superhydrophobicity on a particular substrate are also derived.

Electrospinning superhydrophobic–superoleophilic PVDF‐SiO2 nanofibers membrane for oil–water separation

“…These results indicate that the PVDF‐SiO 2 nanofibers membrane has excellent superhydrophobic–uperlipophilicity. Based on the Wenzel model formula: cosθ r = r(γsg‐γsl)/γgl = rcosθ, the presence of a rough surface means that the actual solid–liquid contact area is larger than that of the geometric contact area, thereby improving the geometrical hydrophobicity [34] …”

Super-Hydrophobic Co–Ni Coating with High Abrasion Resistance Prepared by Electrodeposition

“…The anomalous Co-Ni deposition behavior can be attributed to the formation of Co hydroxyl precipitate, which could hinder the subsequent Ni deposition at the solid/electrolyte interface [24]. Under different thermodynamic and kinetic conditions, the various external crystal morphologies including powder [25], film [26] and dendrite shapes [27,28] could be generated during the electrodeposition process. In our case, increasing the over-potential can favor the development of protrusions in the direction of increasing concentration, therefore leading to the formation of cauliflower-shaped micro-nano structures.…”

Optimization of Patterned Surfaces for Improved Superhydrophobicity through Cost-Effective Large-Scale Computations

“…iq are, c linderi eyc.) b y can be ver compu yationall inyenie for more compulex geomeyriei yhay involve non-monoyonic c rvei and m lti-icale puaterni [26] . The iol tion of yhe Eikonal eq ation doeinty add a coniiderable compu yational load yo yhe overall meyhod beca ie iy ii iolved onl once ay yhe beginning of yhe meyhod.…”