Hierarchical structures have got it rough

In nature, many plants and insects exhibit water-repellent properties. The most well known example is the Lotus leaf (Nelumbo nucifera), with its hierarchically textured surface formed by micrometer-scale papillae on epidermal cells and a superimposed epicuticular wax layer forming nanometer-scale hair-like features [1]. This dual-scale texture combined with chemistry (i.e., the wax) is believed to render the Lotus leaf superhydrophobic, or self-cleaning. This phenomenon, often referred to as the “Lotus effect”, has recently stimulated considerable scientific interest in creating artificial superhydrophobic and/or superoleophobic surfaces.

The Wenzel [2] and Cassie-Baxter [3] models have been cited extensively in the literature to explain the effect of surface roughness on contact angles. Wenzel's model assumes that when a liquid forms a sessile drop on a rough surface, it completely fills the space between surface features. By Wenzel's model, the wetting behavior of a smooth surface will be magnified on a rough surface with the same surface energy. The Cassie-Baxter model assumes that pockets of air are trapped in the surface texture, forming a composite interface between the solid/air and the liquid droplet. By equating these two models, a critical contact angle for transition from the Wenzel state to the Cassie-Baxter state can be derived.

For intrinsic angles greater than the critical angle, the Cassie-Baxter state has lower energy, otherwise the Wenzel state has lower energy. By the Cassie-Baxter model, it is possible for a rough surface to have an apparent contact angle greater than 90° (in a meta-stable state) even if the intrinsic contact angle is less than 90°. This is particularly important for developing oleophobic surfaces since no known materials have equilibrium contact angles greater than 90° for many organic compounds.

A water droplet on the Lotus leaf rolls at the slightest inclination, carrying dirt particles away from the surface. In contrast, some artificial surfaces have been reported to exhibit static contact angles well above 150° for water, yet the droplet remained stuck even as the surface was tilted at 90° or higher. Therefore, to create artificial self-cleaning surfaces, high static contact angles are not sufficient – the contact angle hysteresis must be minimized to allow liquid droplets to readily roll off the surface. Despite numerous attempts to explain contact angle hysteresis on the basis of wet contact area and surface energy or the contact line, the exact mechanism remains unclear. However, it is generally accepted that multi-scale roughness is helpful for lowering contact angle hysteresis, presumably via minimization of the wet contact area and/or formation of a tortuous contact line in three dimensions.

Further Reading
[1] W. Barthlott, C. Neinhuis, Planta, 201 (1997), p. 1
[2] R.N. Wenzel, Ind Eng Chem, 28 (1936), p. 988
[3] A.B.D. Cassie, S. Baxter, T Faraday Soc, 40 (1944), p. 546