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.

Wetting behavior was studied on surfaces with a single, circular heterogeneous island. Lyophobic islands were created on lyophilic Si wafers using polystyrene. Alternately, lyophobic perfluoroalkoxy fluoropolymer film was etched to make lyophilic domains. Contact angles and hysteresis were measured with water and hexadecane. Small sessile drops were deposited on the center of an island and liquid was sequentially added, eventually forcing the contact line to advance beyond the island perimeter onto the surrounding area. Even though the underlying contact area contained a mixture of lyophilic and lyophobic domains, the contact angles, both advancing and receding, were equal to the angles exhibited by the homogeneous periphery. Or in other words, if the heterogeneity was completely contained with the contact area and did not intersect the contact line, then no area averaging of the contact angles occurred. These findings suggest that interactions at the contact line, not the contact area, control wetting of heterogeneous surfaces.

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Very rough surfaces can suspend small liquid drops and produce very large contact angles. This behavior often is referred to as ultralyophobicity or super repellency. It is proposed that two criteria must be met to invoke ultralyophobicity: a contact line density criterion and asperity height criterion. The proposed criteria were tested using experimental data available in the literature and were found to correctly predict suspension of small water drops on model rough surfaces with a wide variety of asperity shapes, sizes, and spacing.