Maximal deformation of an impacting drop

Abstract

We first study the impact of a liquid drop of low viscosity on a super-hydrophobic surface. Denoting the drop size and speed as $D_{0}$ and $U_{0}$, we find that the maximal spreading $D_{\hbox{\scriptsize\it max}}$ scales as $D_{0}\hbox{\it We}^{1/4}$ where We is the Weber number associated with the shock ($\hbox{\it We}\,{\equiv}\,\rho U_{0}^2 D_{0}/\sigma$, where $\rho$ and $\sigma$ are the liquid density and surface tension). This law is also observed to hold on partially wettable surfaces, provided that liquids of low viscosity (such as water) are used. The law is interpreted as resulting from the effective acceleration experienced by the drop during its impact. Viscous drops are also analysed, allowing us to propose a criterion for predicting if the spreading is limited by capillarity, or by viscosity.