Maximum Spread of Droplet on Solid Surface: Low Reynolds and Weber Numbers

Abstract

This theoretical study proposes an analytical model to predict the maximum spread of single droplets on solid surfaces with zero or low Weber and Reynolds numbers. The spreading droplet is assumed as a spherical cap considering low impact velocities. Three spreading states are considered, which include equilibrium spread, maximum spontaneous spread, and maximum spread. Energy conservation is applied to the droplet as a control volume. The model equation contains two viscous dissipation terms, each of which has a defined coefficient. One term is for viscous dissipation in spontaneous spreading and the other one is for viscous dissipation of the initial kinetic energy of the droplet. The new model satisfies the fundamental physics of drop-surface interaction and can be used for droplets impacting on solid surfaces with or without initial kinetic energy.