Impact of line tension on the equilibrium shape of liquid droplets on patterned substrates

We studied the morphology of liquid droplets on substrates with a lateral wettability pattern using numerical calculations. We analyzed the influence of the wettability contrast, the sharpness of the transitions between adjacent hydrophilic and hydrophobic stripes, and the line tension of the three-phase contact line on the modulation amplitude of the latter and on the shape of the liquid-vapor interface. In the presence of lateral variations of the line tension, we found that the modulation of the contact angle along the contact line is controlled by the local wettability of the substrate, by the local curvature of the contact line, and by gradients of the line tension. This result confirms a recently published theoretical extension of the modified Young equation. Furthermore, the numerical calculations demonstrate that and show how the line tension can be extracted from atomic force microscopy measurements of liquid droplets on patterned substrates.