Apparent contact angles on rough surfaces: the Wenzel equation revisited

The thermodynamic status of the Wenzel equation is discussed. It is explained and demonstrated by an example that the Wenzel equation may be incorrect. However, it is mathematically proven for sawtooth surfaces that the Wenzel equation becomes the correct one for the apparent contact angle as the drop size becomes infinitely larger than the scale of the roughness. It is shown, that under this condition the drop becomes axisymmetric even if the roughness of the solid surface is not. A complete proof for rough surfaces in general is also feasible, however the mathematical complexity of this proof is beyond the present scope.