Shapes of drops in the Cassie state on grooved surfaces

Liquids spread anisotropically on grooved surfaces; potential applications include self-cleaning surfaces and digital microfluidics. However, the wetting of grooved surfaces is generally only qualitatively understood. We simulate equilibrium drop shapes in the Cassie (suspended) state on grooved surfaces. It is shown that while inertia is required for drops to advance from one groove to the next, drops recede to near-circular shapes under the influence of surface energy alone. Given the number of grooves on which an advancing drop resides, its shape can be quantitatively predicted and matched to experiment. Such drops spread parallel to the grooves as if on a one-dimensional Cassie surface, which can be used to infer the intrinsic contact angle from the drop shape and groove dimensions. Tapered grooves allow self-propelled unidirectional motion.