An effective dynamic for the edge of a three-dimensional sessile drop is derived from the capillary waves model of two-dimensional interfaces. The corresponding Monte Carlo evolution is implemented to study wetting of a disordered substrate. Hysteresis associated with a stick-slip mechanism is measured as a function of disorder and system size. For a given system size, no measurable hysteresis is found at weak disorder. For a given disorder, even small, a measurable contact angle hysteresis is found above a certain system size.

• Received 1 May 1997

DOI:https://doi.org/10.1103/PhysRevLett.79.3704