Abstract
Contact angle hysteresis on weakly heterogeneous surfaces is studied using an extension of Imry and Ma's analysis of the random field problem. Deformations of the liquid-vapor interface in response to the heterogeneity are characterized by a length Ld which increases as the magnitude of the heterogeneity decreases. The characteristic energy associated with these deformations is used to find the scale of contact angle hysteresis. In the absence of gravity, contact angle hysteresis occurs for arbitrarily weak heterogeneity. Hysteresis disappears when Ld exceeds the gravitational capillary length, while systems with characteristic size less than Ld show increased hysteresis.