A Cassie-like law using triple phase boundary line fractions for faceted droplets on chemically heterogeneous surfaces.

We present experimental contact angle data for surfaces, which were surface-engineered with a hydrophobic micropattern of hexagonal geometry. The chemically heterogeneous surface of the same hexagonal pattern of defects resulted in faceted droplets of hexagonal shape. When measuring the advancing contact angles with a viewing position aligned parallel to rows of defects, we found that an area averaged Cassie-law failed in describing the data. By replacing the area fractions by line fractions of the triple phase boundary line segments in the Cassie equation, we found excellent agreement with data.