Analytical consideration of liquid droplet impingement on solid surfaces

In industrial applications involving spray-cooling, combustion, and so on, prediction of the maximum spreading diameter of a droplet impinging on a solid surface permits a quantitative estimation of heat removal and energy consumption. However, although there are many experimental studies regarding droplet impingement behaviour, theoretical models have an applicability limit for predicting the maximum spreading diameter. In the present study, we have developed an analytical model for droplet impingement based on energy conservation that considers adhesion energy in both horizontal and vertical directions at the contact line. The theory is validated by our experiment and existing experimental data possessing a wide range of Weber numbers. We demonstrate that our model can predict β _m (i.e., the maximum spreading diameter normalised in terms of initial droplet diameter) for various Newtonian liquids ranging from micro- to millimetre-sized droplets on different solid surfaces and can determine the transition between capillary and viscous regimes. Furthermore, theoretical relations for scaling laws observed by many researchers are derived.