Apparent contact angles for reactive wetting of smooth, rough, and heterogeneous surfaces calculated from the variational principles

Apparent steady contact angles inherent for reactive wetting of flat, rough and chemically heterogeneous solid surfaces are calculated from the variational analysis of the reactive wetting problem. The surface (2D) and linear (1D) contributions to the free energy of the reactive wetting system constitute the apparent contact angle, whereas the bulk contributions such as external fields and heat release do not influence the apparent contact angles of reactive wetting. When the interfacial tensions constitute the apparent contact angle, the equilibrium contact angles are independent on the dimensions of droplets. When the line tension is taken into account, the apparent steady contact angle depends on the radius of the contact area. The Wenzel and Cassie-like regimes of reactive wetting are considered. Reactive wetting of porous surfaces is addressed. The Cassie impregnating reactive wetting regime is treated.