Marangoni and Variable Viscosity Phenomena in Picoliter Size Solder Droplet Deposition

This paper focuses on the effect that surface tension (Marangoni phenomenon) and viscosity dependence on temperature has on the spreading, transient behavior and final post-solidification shape of a molten Sn63Pb solder droplet deposited on a flat substrate. A Lagrangian finite element formulation of the complete axisymmetric Navier-Stokes equations is utilized for the description of the droplet behavior. Linear temperature dependence for the surface tension and an exponential dependence for the viscosity are assumed. The initial droplet temperature is varied in 50 K steps from 200°C to 500°C, whereas the substrate temperature is kept constant at 25°C. This varies the initial Reynolds number $Re0$ from 360 to 716 and the Marangoni number Ma from −9 to −49. The initial Weber number $We0$ and initial Prandtl number $Pr0$ are for all cases O(1) and $O10−2,$ respectively. The impact velocity and the droplet diameter remain unchanged in all cases examined at 1.5 m/s and 80 microns. A major finding of the work is that, contrary to intuition, the Marangoni effect decreased droplet spreading monotonically. Due to the Marangoni effect, the mechanism that arrested spreading is the surface tension and not the beginning of freezing. Droplet receding during recoiling was aided by the Marangoni effect. On the other hand, the change of viscosity with temperature showed no significant influence on the outcome of the droplet impact.