At contact angles below 90°, wetting of the surface is energetically advantageous overall for the two phases involved. Since a rough material has a larger total surface area than a smooth one due to the tiny depressions and thus offers a larger wetting area, the wettability increases.

Fresnel Blender

This wetting behavior is also known as the lotus effect since the lotus leaf is one of the least wettable non-technical surfaces. There are many industrial applications for superhydrophobic materials or coatings, for example for fouling and wetness protection or for self-cleaning textiles or building walls.

Roughness (surface roughness) is the degree of unevenness of a solid surface below the size scale of its shape or waviness, but above the irregularity of crystal lattice structures. The roughness has an influence on the wettability of a solid.

The Fresnel or Dielectric Fresnel node computes how much light is reflected off a layer, where the rest will be refracted through the layer. The resulting weight can be used for layering shaders with the Mix Shader node. It is dependent on the angle between the surface normal and the viewing direction.

Fresnel Light

where θ* is the measured contact angle. This is called the apparent contact angle for a rough surface because it is the angle of the droplet contour with an apparently straight profile line. θ is the contact angle that would exist on a smooth surface of the same material and corresponds to the ideal contact angle according to Young's equation. r' is called the roughness coefficient and indicates the ratio of the total surface area to the surface geometrically projected onto a plane.

Fresnel pronunciation

The most common use is to mix between two BSDFs using it as a blending factor in a Mix Shader node. For a simple glass material you would mix between a glossy refraction and glossy reflection. At grazing angles more light will be reflected than refracted as happens in reality.

The use of this effect is part of everyday practical knowledge, for example when components are ground before painting or bonding to increase wetting and adhesion. For surface tension measurements using the Wilhelmy plate method, the platinum plate is roughened to optimize wetting by the sample.

[3] P. Swolana, Ch. Weigel, T. Geiling, L. Dittrich, D. Frese: Wetting and roughness - What to do if Wenzel does not work? KRÜSS Application Report AR295, 2020.

Fresnel lens

Based on the Wenzel equation, it can be seen why the critical angle for the transition from wetting enhancement to reduction is 90°. Since cos θ assumes negative values above 90°, the apparent contact angle becomes larger. However, the Wenzel equation can then be applied only to a limited extent because, at low wetting, not all the depressions of the rough surface are usually filled with liquid. Cassie and Baxter [2] have formulated the following relationship for a condition where only parts of the entire surface are in contact with the liquid:

Fresnel effect

Result parameters for roughness and suitable measuring methods are defined in the ISO 25178 standard. Non-destructive measurements by non-contact optical methods, for example confocal microscopy, should be emphasized. Other methods use, for example, an air stream or even vacuum and make use of the gas permeability on contact between a smooth and a rough surface.

Roughness affects the wettability of a solid and thus the contact angle of a liquid as well as adhesion. A rule of thumb states that roughness improves wettability at small contact angles (angle becomes smaller), and reduces it at large contact angles (angle becomes larger). The limiting contact angle of wettability, which determines the deflection in one direction or the other, is 90°. The roughness-related reduction in wetting comes into play on superhydrophobic surfaces; it is often referred to as the Lotus Effect.

For a two-layered material with a diffuse base and a glossy coating, you can use the same setup, mixing between a diffuse and glossy BSDF. By using the Fresnel as the blending factor you are specifying that any light which is refracted through the glossy coating layer would hit the diffuse base and be reflected off that.

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Extremely low wettability, also known as superhydrophobicity, results from the rough surface texture of a material where the smooth surface is already non-wettable. Put simply, the liquid avoids the depressions in the surface, which is enlarged by roughness, instead of filling them up. The technical term for this effect is capillary depression in contrast to capillary adhesion - in an unwettable capillary, the capillary force does not pull the liquid inward, but pushes it outward.

It seems to be obvious to calculate a "roughness-corrected" contact angle using the Wenzel formula in order not to have to investigate the roughness influence on wetting separately. In practice, however, such an approach is fraught with great uncertainties. A study carried out by KRÜSS [3] on the basis of surfaces with defined roughness shows that the roughness influence can deviate considerably from the behavior to be expected according to Wenzel - up to a trend reversal, in which a well-wettable material is less wetted in the rough state.