Criteria for entrapped gas under a drop on an ultrahydrophobic surface

Ultrahydrophobicity of a rough surface is mainly attributed to the entrapped gas under a drop. Two criteria were proposed for the entrapped gas: an intruding angle criterion and an intruding depth criterion. These two criteria are that the intruding angle must be less than the maximum asperity slope angle and the intruding depth must be less than the height of the asperities. The intruding angle is determined by the true contact angle, the surface geometry, and the drop size. The intruding angle is directly proportional to the true contact angle, and it increases with an increase of the fractional area of the liquid-gas interface under the drop and with a decrease of the linear dimension of the three-phase contact line on the asperities. The effect of the drop size on the intruding angle is induced by Laplace and hydrostatic pressures. The intruding depth increases with an increase of the intruding angle and the distance between the asperities. The proposed criteria were evaluated using experiment data from the literature. Comparison between the experiment and calculation results showed that the experiment data supported the theory.