Investigation on droplet spreading and energy conversion process on solid surface with low impinging velocity

Accurately and quantitatively tracking the droplet impinging and spreading process in theory is of paramount importance for informing and advancing engineering application. However, the existing models have problems such as large energy calculation deviations and imprecise shape hypotheses, which lead to significant theoretical errors and require in-depth correction. In this paper, a numerical model based on the laminar flow equation coupled phase field method and the dynamic contact angle model involved in the droplet impinging and spreading process is first developed and validated. The morphology and parameters of droplet spreading at various conditions and the role and influence of gravitational potential energy are further investigated. Subsequently, a semi-empirical modified spoon-like model grounded in numerical outcomes and attempting to overcome traditional assumptions limitations is advanced, with its practical applicability rigorously discussed. Results show that the droplet spreading process basically undergoes “round sphere”, “round cap”, and “pancake-like /cylinder-like” to “shallow bottomed round tray”. Changes in Weber number (We) and equilibrium contact angle (θe) marginally alter the duration, spreading size, and droplet morphology characteristics in each process. The impact of gravitational potential energy is notably modulated by process parameters, exhibiting an increase with escalating droplet diameter and density, while decreasing in response to heightened initial droplet velocity and surface tension coefficients. Conversely, it remains largely invariant to changes in droplet viscosity and equilibrium contact angle. The consideration of shape factor and viscosity modification factor allows the surface energy and viscous dissipation energy to be accurately defined, making the proposed semi-empirical modified spoon-like model exhibit good performance, for all 65 studied cases the relative errors of droplet maximum spreading length factor (βmax) and center thickness (h) fall essentially within the 5% and 10% interval respectively.