A theoretical approach to characterize the superhydrophobic properties of randomly rough surfaces

In this paper, a simple theoretical method is developed in order to characterize the superhydrophobic properties of rough surfaces. The size of the apparent liquid-solid contact area is assumed much larger than the micromorphology of the substrate, and the presence of a composite interface at the microscale is also assumed. Results show superhydrophobic properties are strongly affected by the Wenzel roughness parameter rW. Vice versa, the drop volume negligibly influences the apparent contact angle at the macroscale, at least in the range of volumes that we usually have for liquid droplets. Indeed, in this range, the interfacial pressure takes values that are not sufficiently high to significantly affect the liquid-Air interface.