THE ACTUAL CONTACT-ANGLE ON A HETEROGENEOUS ROUGH-SURFACE IN 3 DIMENSIONS

A general equation is presented for the actual contact angle on a soli d surface in a three-dimensional setting. The solid surface may be rou gh or heterogeneous or both. The effects of the existence of line tens ion and its variation with the position of the contact line are also i ncluded. It is shown that when line tension can be ignored, the actual contact angle at each point on the solid surface always equals the in trinsic contact angle (which is given in this case by the Young equati on). However, when line tension is significant, the actual contact ang le deviates from the Young contact angle by a term proportional to the geodesic curvature of the contact line and a term depending on the di rectional derivative of the line tension. Various situations are prese nted and discussed. Of particular interest is the example of a drop on a sphere, for which it is shown that the actual contact angle equals the Young contact angle when the contact line coincides with the equat or of the sphere.