Stable drop shapes under disjoining pressure. I. A hierarchical approach and application

The contact line region as affected by the disjoining pressure has been analyzed under the assumption that it can sustain only two types of profiles. Disjoining pressure represents the extra potential in thin films that always exists in the contact angle region where a liquid drop or a wedge thins to meet the solid substrate and in turn affects the contact angle as well as the film profile. It is shown here that the integration of the augmented Young-Laplace equation to yield the above types of drop profiles under the action of disjoining pressure leads to the usual conditions of equilibrium as well as the condition of stability in the same analysis. Other inequality constraints are obtained where the stability condition does not apply. The fact that stability condition coexists with the conditions of equilibrium is pursued to show in one case that the stability modifies half of the predicted outcomes in the drop shapes. In addition, exceptions to the rule are found, which are physically meaningful, and a scale-dependent equilibrium is reported for the first time.