Abstract

Interface is where the macroscopic meets the microscopic; even a simple fluid becomes there a complex fluid. The origins of surface tension and disjoining pressure lie in nanoscale density gradients governed by molecular interactions. We shall see how the paradox of the moving contact line is resolved on the molecular scale when it is viewed as a physico-chemical problem dependent on fluidsubstrate interactions.

There is enormous scale separation between molecular and hydrodynamic scales, which makes computation difficult but facilitates analytical theory. We ascend from molecular to macroscopic scales – from density functional theory to lubrication equations – by the approximation ladder. Multiscale perturbation theory elucidates dynamics of the contact line and provides tools for the study of various instabilities, as demonstrated taking as an example the motion of droplets driven by surface forces.