Splash Criteria for Liquid Drop Impact on Smooth, Dry Surfaces

It is important to find a criterion that predicts the transition from smooth deposition to splashing of low-viscosity liquid drops when they land on a smooth, dry surface. Using high-speed imaging, we have determined the threshold pressure, $P_T$, of the ambient gas for which a liquid drop splashes as a function of the relevant parameters (gas molecular weight $m_G$, liquid viscosity $\nu_L$, surface tension $\sigma$, drop diameter D, and impact speed $U_0$). There is a non-monotonic trend of $P_T$ versus $U_0$ [1]. We find this same trend as we systematically change other liquid and gas properties; they simply shift the curve. By defining a scaled pressure, $P_{T,scaled}=P_T D^{0.5} \nu_L^{0.25} m_G^{0.5} \sigma^{-0.25}$, and scaled impact speed $U_{0,scaled}=U_0 D^{0.3} \nu_L^{0.4} \sigma^{-0.35}$, we find a collapse of all data sets onto a single curve. This scaling applies to both high and low velocity regimes.\\[4pt] [1] {Xu} L. Xu, S. Nagel, and W. Zhang. Phys. Rev. Lett. 94, 184505 (2005).