Energetics of spreading droplets and role of capillary waves at low Weber numbers below 10

Abstract

In this study, we investigate the energy conversion and dissipation mechanisms of spreading droplets on a solid surface at a low Weber number regime, which neither conventional energy-balance-based theories nor empirical scaling laws can completely explain. The energetic analysis presented in this study shows that on a hydrophilic surface, the actual primary energy source driving the spreading process is the initial surface energy not the initial kinetic energy. The conventional energy-balance-based approaches are found to be valid only for the spreading process on a hydrophobic surface. Particular attention is also paid to the roles of the capillary waves. The capillary waves are found to play significant roles in all of the important flow physics, that is, the interfacial structure, the oscillatory motions and the rapid collapse of the liquid film, the onset of the viscous regime, and the energy loss mechanism. It is also shown that the energy dissipation caused by the capillary-wave-induced phenomena can be estimated to be 25%–35% and 55%–65% of the total energy loss for a hydrophilic and a hydrophobic surface, respectively, at the low Weber number regime.