Contact Angle Hysteresis on a Heterogeneous Surface: Solution in the Limit of a Weakly Distorted Contact Line

In the case of a weakly distorted contact line, we construct a one-variable equation giving the metastable configurations of a fluid interface in contact with a heterogeneous solid surface. In this limit it is possible to study the contact angle hysteresis created by semi-concentrated assemblies of individual defects. The results exhibit many collective effects, some of which can be described by a convenient renormalization of the hysteresis threshold and of the defect density. They are consistent with available experimental data.