Super-hydrophobic surfaces, as well as, low adhesion and friction are desirable for various industrial applications. Hydrophobic (water-repellent) surfaces can be constructed either by using low surface energy materials or by chemically treating surfaces with materials such as polytretafluoroethylene, silicon, or wax. Another technique that can be used to increase the hydrophobic properties of a hydrophobic surface is to increase the surface area by increasing surface roughness. If a surface is initially hydrophilic, then introducing roughness to that surface will make it even more hydrophilic. Wetting (hydrophilic property) is characterized by the contact angle of a surface and occurs when the surfaces has a contact angle of θ < 90°, whereas if the surface is hydrophobic, the value of the contact angle is greater than 90°. The contact angle depends on several factors, such as roughness, the manner of surface preparation, and surface cleanliness (Adamson, 1990; Israelachvili, 1992; Bhushan, 1999, 2002, 2005).
Models have been presented in the past to determine how roughness affects hydrophobicity. Wenzel (1936) developed the first model, which is based on the consideration of net energy decrease during spreading of a droplet on a rough surface. A rough surface has larger solid-liquid interface area, leading to larger net energy, and it is responsible for the increase of contact angle for a hydrophobic surface and the decrease of the contact angle for a hydrophilic surface. Wenzel developed an equation that relates the roughness with the contact angles of a flat surface of a certain material and that of the rough surface of the same material and is given by: Cos θ = Rf cos θo
where θ = contact angle of a rough surface, θo = contact angle of a flat surface, and Rf = roughness factor of the rough surface. The roughness factor is defined as the ratio of the total surface area of the rough surface and the projected area of the rough surface...
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