Wetting in the nanoscale: a continuum mechanics approach

A continuum mechanics model has been developed to study the equilibrium shape of nanometric droplets on a planar solid substrate and how, in this scale, the contact angle depends on the drop size. The drop is modeled as a liquid volume enclosed in an inextensible membrane, subject to an isotropic tension (the surface tension) and to a field of surface forces including, in the proximity of the solid, the liquid-to-solid interactions, envisaged as a generic potential force per unit surface directed normally to the solid surface (i.e. vertically). The only conditions required to solve the problem are those of mechanical and thermodynamic equilibrium. The predictions of the model are discussed in comparison with data on nanodrops retrieved by a special AFM device for a number of different liquid-solid systems.