Marangoni and temperature dependent wetting phenomena in picoliter size solder droplet deposition

The effect of the temperature dependence of surface tension (Marangoni effect) and of the wetting phenomenon on the spreading and final post-solidification shape of a molten Sn63Pb solder droplet deposited on a flat substrate is investigated. A Lagrangian finite element formulation of the complete axisymmetric Navier-Stokes equations is utilized for the description of the droplet behavior. Linear temperature dependence of the surface tension and a wetting model based on a balance of the interfacial tensions at the contact line are assumed. The droplet superheat is varied in steps of 100K from 200oC to 500oC, whereby the Marangoni number Ma alters from –9 to –49. The initial Weber number We0 and initial Prandtl number Pr0 are for all cases O(1) and O(10), respectively. The initial impact velocity and the droplet diameter remain unchanged in all cases examined at 1.5 m/s and 80 microns. A novel adaptive mesh refinement is employed and the results are compared to those obtained earlier with a fixed grid size and the Navier-Slip condition applied at the contact line.