Wenzelmodellen

Wenzelmodellen, commonly referred to as the Wenzel model, is a theory in wettability describing how roughness influences the apparent contact angle of a liquid on a solid surface. It was proposed by Robert N. Wenzel in 1936. The model gives the relationship cos theta* = r cos theta, where theta* is the apparent contact angle on the rough surface, theta is the intrinsic contact angle on a smooth surface, and r is the roughness factor, defined as the ratio of the actual surface area to the projected (planar) area of the surface. By definition, r > 1 for rough surfaces.

Assumptions and interpretation: The Wenzel model assumes a chemically homogeneous surface and complete wetting of the roughness, meaning the liquid fully conforms to the surface with no air pockets. Under these conditions, roughness amplifies wettability: if theta < 90°, increasing r decreases theta* (more wetting); if theta > 90°, increasing r increases theta* (more non-wetting).

Applications and limitations: The model is used to predict and design wettability for coatings, textiles, and microfluidic devices where surface roughness is engineered to enhance or reduce wetting. It is valid only when the liquid penetrates the roughness completely and there is no air entrapment. It does not account for chemical heterogeneity, hysteresis, or dynamic effects, and it can fail when air pockets or composite surface states occur.

Relation to other models: The Wenzel model contrasts with the Cassie–Baxter model, which applies to heterogeneous surfaces where air pockets are trapped. See also: contact angle, wettability, roughness factor, Cassie–Baxter equation.

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