Analytical model for predicting maximum spread of droplet impinging on solid surfaces

Abstract

In the present study, we develop a theoretical approach to predict the maximum spread of a liquid droplet on a dry solid surface. By using the dynamics of the gas layer entrapped underneath the droplet during initial stages of spreading, we determine the initial spread velocity of the droplet. The predicted spread velocity is used to model viscous dissipation and spread time of the droplet, post-impact. We also reformulate the surface energy of the droplet at the maximum spread to account for the presence of a rim formed at the periphery of the droplet. Incorporating the renewed terms into an energy conservation equation, the maximum spread of the droplet is predicted. The constructed model is validated with both the in-house experiments and the literature performed for various liquids and surfaces. The study also examines the existing scaling laws available to predict the maximum spread in inertial and viscous regimes and compares them with the model. Results reveal that the proposed model effectively predicts maximum spread values even at a low Weber number, despite variations in wettability values. The scaling laws were found to be inefficient in predicting the maximum spread for water at a low Weber number as they do not account for the effect of the surface wettability.