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We consider a three-dimensional liquid drop sitting on a rough and chemically heterogeneous substrate. Using a novel minimization technique on the free energy of this system, a generalized Young's equation for the contact angle is found. In certain limits, the Cassie and Wenzel laws, and a new equivalent rule, applicable in general, are derived. We also propose an equation in the same spirit as these results but valid on a more “microscopic” level. Throughout we work under the presence of gravity and keep account of line tension terms.

Contact Angles on Heterogeneous Surfaces: A New Look at Cassie's and Wenzel's Laws