On the usefulness of the equation of state approach for contact angles on rough surfaces

The equation of state (EQS) approach has been used successfully to calculate the surface tension of solids for flat surfaces where only the effects of the tensions involved are dominant and define the wettability. In this work we use the EQS approach to modelate the wetting by ethylene glycol, glycerol, and water on homogeneous polymer rough surfaces. The surfaces were made of polystyrene using the phase separation method and topographically characterized by atomic force microscopy through the area factor (ra\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${r}_{\text {a}}$$\end{document}). We also defined an effective surface tension γsv′\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\gamma'_{{\text {sv}}}$$\end{document}, which decreases with the roughness and it explains the increasing of the contact angle for these surfaces.