Model for Contact Angles and Hysteresis on Rough and Ultraphobic Surfaces

Very rough surfaces can suspend small water drops, prevent wetting, and cause contact angles to approach 180°. A criterion based on contact line density is proposed for predicting the conditions that produce these ultrahydrophobic surfaces, where, above a critical value, drops are suspended by asperities. Critical values of the contact line density can be calculated from contact angles, asperity shape, and information about the contact liquid, such as density and surface tension. The criterion was found to correctly predict suspension for several model surfaces prepared by lithography techniques. Apparent contact angles from suspended and collapsed drops also were modeled by accounting for rough edges and employing a linear average of contact angle along the perimeter of the drop, rather than an area average of cosine. This linear model suggests that, for suspended drops, both advancing and receding angles should increase. Alternatively, for drops that have collapsed over surface asperities, advancing contact angles should increase, while receding angles should decrease. These findings agree with the observations of a number of investigators that have suggested that asperity height may be less important than asperity shape in determining wetting.