Freezing dynamics of molten solder droplets impacting onto flat substratesin reduced gravity

The axisymmetric impingement of solidifying molten solder droplets onto smo oth metallic substrates in a reduced gravity environment is investigated nu merically to provide basic information on the heat and fluid flow phenomena and determine the governing parameters of the process. The numerical predi ctions are also tested against experimental data. Millimeter-sized droplet impact events in reduced gravity are employed for scale up modeling of the impingement of picoliter size droplets of molten eutectic 63%Sn-37%Pb solde r used in electronic chip packaging. The present article reports on both nu merical (the main focus of the paper) as well as experimental work (for the purpose of verification). To this end, the employed numerical model consid ers the axisymmetric impact and subsequent solidification of an initially s pherical, molten solder droplet on a flat, smooth, metallic substrate. The laminar Navier-Stokes equations, combined with the energy transport equatio ns are solved simultaneously in the liquid region (melt) using a Lagrangian approach. In the solid (substrate and solidified droplet material) the hea t conduction equation is solved. A time and space averaged (but phase depen dent) model of the thermal contact resistance between the impacting droplet and the substrate is also incorporated in the formulation. The numerical m odel is solved using a Galerkin finite element method, where a deforming, a daptive triangular-element mesh is employed to accurately simulate the larg e-domain deformations caused by the spreading and recoiling of the impingin g droplet fluid. The experimental work has been conducted in reduced gravit y in the range 2 x 10(-4) to 5 x 10(-4) g with technically relevant impact velocities of similar to 0.2 m/s, in order to provide validation of the num erical predictions. These impact conditions correspond to Re = O(100), We = O(1), and Fr = O(10,000), Ca = O(0.001). Presentation of the numerical res ults in terms of the Froude and the Ohnesorge numbers aids their interpreta tion. Among the results that stand out is the formation of a large number o f frozen ripples on the droplet surface as a result of the simultaneous man ifestation of rapid fluid oscillations and solidification. Furthermore, a n on-intuitive behavior of the solidification times is reported. Specifically , the dependence of the solidification time on the Froude number is not mon otonic, but features a minimum for each distinct value of Ohnesorge number considered in this study. Despite the complexity of the phenomena, the nume rical model captures well the main features of the experimental results. In addition, the model offers key insights on the influence of the Ohnesorge and Froude numbers on the dynamics of the solidification process. (C) 2001 Elsevier Science Ltd. All rights reserved.