Sessile drops: spreading versus evaporation–condensation

Abstract

The equations that govern the dynamics of the liquid–vapor interface and contact line of a sessile drop in the spreading and evaporation–condensation regimes are derived. During spreading, the liquid–vapor interface and contact line convect with the liquid and are therefore material. In contrast, when evaporation or condensation occurs, the liquid–vapor interface and contact line migrate relative to the liquid and are therefore nonmaterial. For spreading, the evolution equations consist of kinematical constraints on the normal velocities of the liquid–vapor interface and contact line along with the normal and tangential components of the constitutively augmented standard force balances on the liquid–vapor interface and along the contact line. The tangential components of the standard force balances on the liquid–vapor interface and at the contact line, being solely dissipative, are automatically satisfied at equilibrium. The normal component of the standard force balance on the liquid–vapor interface reduces to the Young–Laplace equation, whereas its counterpart along the contact line simplifies to the generalization, accounting for line energy, of the Young equation mentioned by Gibbs. In the presence of evaporation or condensation, the kinematical constraints are no longer valid. Their absence is compensated for by the normal components of the configurational force balances on the liquid–vapor interface and along the contact line. Hence, away from equilibrium and in the presence of dissipation, a complete description of the liquid–vapor interface and contact line of a volatile drop involves the normal and tangential components of the standard force balances along with the normal components of the configurational force balances. At equilibrium, the normal component of the configurational force balance on the liquid–vapor interface simplifies to the condition for chemical equilibrium requiring the continuity of the chemical potential, whereas its counterpart along the contact line, being entirely dissipative, holds trivially. Comparison with recently proposed kinetic laws for the liquid–vapor interface and contact line of a drop is provided.