Droplet Spreading: Partial Wetting Regime Revisited

We study the time evolution of a sessile liquid droplet, which is initially put onto a solid surface in a non-equilibrium configuration and then evolves towards its equilibrium shape. We adapt here the standard approach to the dynamics of mechanical dissipative systems, in which the driving force, i.e. the gradient of the system's Lagrangian function, is balanced against the rate of the dissipation function. In our case the driving force is the loss of the droplet's free energy due to the increase of its base radius, while the dissipation occurs due to viscous flows in the core of the droplet and due to frictional processes in the vicinity of the advancing contact line, associated with attachment of fluid particles to solid. Within this approach we derive closed-form equations for the evolution of the droplet's base radius, and specify several regimes at which different dissipation channels dominate. Our analytical predictions compare very well with experimental data.