Effect of Gravity on the Configuration of Droplets on Two-Dimensional Physically Patterned Surfaces

Wetting of solid surfaces is important for many potential applications, including the design of low-drag and antifouling/self-cleaning surfaces, and it is usually quantified by the contact angle and by contact angle hysteresis. Both the chemistry and the physical patterning of the surface are known to affect the contact angle. In studying the wetting of such surfaces, most models focus on the small Bond number (Bo) limit in which the effect of gravity is negligible, which simplifies free energy calculations. In this work, we employ a thermodynamic model for surfaces patterned with two-dimensional asperities, which remains applicable for nonzero Bo. We employ two versions of the model: one in which we require the liquid-vapor interface to remain a circular cap, and another in which we allow the liquid-vapor interface to deform. We find that the effects of gravity are twofold. First, drops with larger Bo tend to flatten and spread across the surface relative to the same size drops with Bo = 0. Second, gravity makes it more favorable for drops to penetrate surface asperities compared to the case of Bo = 0, which also tends to lower the contact angles. The main effect of droplet deformation is to produce larger contact angles for the same wetting configuration. Finally, we compare our model predictions with relevant experimental observations. We find very close agreement with the experiments, thereby validating our theoretical model.