Role of Viscous Dissipative Processes on the Wetting of Textured Surfaces

We investigate the role of viscous forces on the wetting of hydrophobic, semi-hydrophobic, and hydrophilic textured surfaces as second-order effects. We show that during the initial contact, the transition from inertia- to viscous-dominant regime occurs regardless of their surface topography and chemistry. Furthermore, we demonstrate the effect of viscosity on the apparent contact angle under quasi-static conditions by modulating the ratio of a water/glycerol mixture and show the effect of viscosity, especially on the semi-hydrophobic and hydrophobic textured substrates. The reason why the viscous force does not affect the apparent contact angle of the hydrophilic surface is explained based on the relationship between the disjoining pressure and surface chemistry. We further propose a wetting model that can predict the apparent contact angle of a liquid drop on a textured substrate by incorporating a viscous force component in the force balance equation. This model can predict apparent contact angles on semi-hydrophobic and hydrophobic textured surfaces exhibiting Wenzel state more accurately than the Wenzel model, indicating the importance of viscous forces in determining the apparent contact angle. The modified model can be applied for estimating the wetting properties of arbitrary engineered surfaces.