# Rough Surfaces Wenzels Model

The influence of the substrate surface roughness on wetting was first described by the well-known thermodynamic approach of Wenzel. The Wenzel equation for the contact angle on a rough surface is defined by the following equation:

where 0 is the observed contact angle on a rough surface and 00 is its contact angle on a smooth surface. The roughness ratio, r is defined as the ratio of the surface area ASL to its flat projected area AF (Fig. 8.7a)

This simple relationship predicts that as roughness increases, a hydrophobic surface (00 > 90°) becomes more hydrophobic, while a hydrophilic (00 < 90°) surface becomes more hydrophilic. According to Wenzel equation polymers such as Polyvinyl chloride (PVC) and Polyethylene terephthalate (PET) with 00 < 90°,

Fig. 8.7 Schematic illustration of a liquid droplet in a homogeneous (Wenzel), b heterogeneous (Cassie-Baxter) wetting regimes

Fig. 8.7 Schematic illustration of a liquid droplet in a homogeneous (Wenzel), b heterogeneous (Cassie-Baxter) wetting regimes

should become more hydrophilic by introduction of surface roughness. However, highly hydrophobic surfaces have been fabricated from these polymers by increasing the surface roughness, indicating that the Wenzel equation fails to predict the water contact angle of these surfaces [48, 82].

Continue reading here: Heterogeneous Surfaces Cassie Baxter Model

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