When Wenzel and Cassie Are Right: Reconciling Local and Global Considerations

The condition under which the Wenzel or Cassie equation correctly estimates the most stable contact angle is reiterated and demonstrated: these equations do hold when the drop size is sufficiently large compared with the wavelength of roughness or chemical heterogeneity. The numerical demonstrations somewhat mimic recent experiments that seemingly refuted the Wenzel and Cassie equations and show that these experiments were performed only for drops of sizes similar in order of magnitude to the wavelength of roughness or chemical heterogeneity. Under such conditions, the Wenzel and Cassie equations are a priori not expected to be valid. It is also explained that both the local equilibrium condition at the contact line and the global equilibrium condition involving the wetted area within the contact line are necessary and complementary.