A Numerical Correlation for The Solidification of Liquid Metal Droplets Impacting onto a Substrate

The problem of normal incidence impact with solidification of a spherical liquid metal droplet onto a rigid planar substrate is studied. The Navier-Stokes equations are solved using a finite-volume formulation with a fixed grid. The free surface of the droplet is tracked by the Volume of Fluid (VOF) method. The surface tension on the droplet surface is evaluated by a Continuum Surface Force (CSF) model. The energy equation which includes both convection-diffusion heat transfer and a mushy-region for the phase change (solidification) is modeled by using an enthalpy-based formulation. The method developed provides a comprehensive model of the dynamic and thermal aspects of the impact process. A parametric study has been performed. The effects of several parameters on the spread of the droplet on the substrate are determined. The information is used to develop, via dimensional analysis, a relationship between non-dimensional numbers and the spread factor. A correlation that predicts the spread factor as a function of some non-dimensional numbers is obtained which can serve as a design tool for liquid metal jetting applications. The correlation agrees with the experimental data available in the literature suggesting that the basic impact mechanics have been captured in the numerical model.