Three-dimensional presolidification heat transfer and fluid dynamics in molten microdroplet deposition

The non-axisymmetric, coupled fluid mechanics and heat transfer of an impacting liquid solder droplet on a flat substrate is investigated numerically using the finite element method. The modelling of the fluid mechanics is based upon the full laminar Navier–Stokes equations employing a Lagrangian frame of reference. Due to the large droplet deformation, the surface (skin) as well as the volumetric mesh have to be regenerated during the calculations in order to maintain the high accuracy of the numerical scheme. The pressure and velocity fields are then interpolated on the newly created mesh. The energy equation is solved in both the droplet and the substrate domain. A time and space averaged thermal contact resistance is implemented between the two thermal domains (droplet and substrate). For the impact parameters used in this study (typical values We=2.38, Fr=16,300, Re=157), the droplet rolls along the substrate but its shape remains practically axisymmetric for all the impact angles within the range from 0° to 60°. The substrate/droplet contact area is not a monotonically decreasing function of time and the cooling of the droplet is markedly dependent on the impact angle.