Apparent contact angle of drops on liquid infused surfaces: geometric interpretation

We theoretically investigate the apparent contact angle of drops on liquid infused surfaces as a function of the relative size of the wetting ridge and the deposited drop. We provide an intuitive geometrical interpretation whereby the variation in the apparent contact angle is due to the rotation of the Neumann triangle at the lubricant-drop-gas contact line. We also derive linear and quadratic corrections to the apparent contact angle as power series expansion in terms of pressure differences between the lubricant, drop and gas phases. These expressions are much simpler and more compact compared to those previously derived by Semprebon et al. [ Soft Matter , 2017, 13 , 101-110]. We provide an intuitive geometrical interpretation for the apparent contact angle on LISs, due to the rotation of the Neumann triangle at the lubricant-droplet-gas contact line.