Marangoni and Variable Viscosity Phenomena in Picoliter Size Solder Droplet Deposition

This numerical investigation studied the effects which the temperature dependence of surface tension (Marangoni phenomenon) and viscosity has on the spreading, the 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 was utilized for the description of the droplet behavior. Linear temperature dependence for the surface tension and an exponential dependence for the viscosity were assumed. The initial droplet temperature was varied in 50K steps from 200°C to 500°C, whereas the substrate temperature was kept constant at 25°C. This varied 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 were for all cases O(1) and O(10⁻²), respectively. The impact velocity and the droplet diameter remained unchanged in all cases examined at 1.5 m/s and 80 microns. A major finding of the work was that, contrary to intuition, the Marangoni effect decreased droplet spreading monotonically. Due to the Marangoni effect, surface tension forces instead of freezing arrested spreading. 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.