Statistical theory of wetting of liquid drops on superhydrophobic randomly rough surfaces

It is well known that hydrophobic surfaces may become superhydrophobic when their surface is properly roughened. However, the role of roughness is not yet very clear, notwithstanding several theoretical and experimental investigations. In the present paper, we propose a relatively simple theory aiming at calculating the apparent contact angle (ACA) and the contact area occurring in the case of drops gently deposited on two-dimensional randomly rough surfaces. Our theory applies both to isotropic and anisotropic rough surfaces, although in the latter case the predicted ACA has to be interpreted as the average contact angle at the triple line. We assume large separation of scales, i.e., that the spectral content of the surface lies in a range of wavelengths much smaller than the size of the apparent liquid-solid contact area. Results show that anisotropy negligibly affects the ACA, and a very reasonable agreement is obtained between theoretical ACA values and experimental data.