Freezing dynamics of molten solder droplets impacting onto flat substrates in reduced gravity

Abstract

The axisymmetric impingement of solidifying molten solder droplets onto smooth metallic substrates in a reduced gravity environment is investigated numerically to provide basic information on the heat and fluid flow phenomena and determine the governing parameters of the process. The numerical predictions 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 solder used in electronic chip packaging. The present article reports on both numerical (the main focus of the paper) as well as experimental work (for the purpose of verification). To this end, the employed numerical model considers the axisymmetric impact and subsequent solidification of an initially spherical, molten solder droplet on a flat, smooth, metallic substrate. The laminar Navier–Stokes equations, combined with the energy transport equations are solved simultaneously in the liquid region (melt) using a Lagrangian approach. In the solid (substrate and solidified droplet material) the heat conduction equation is solved. A time and space averaged (but phase dependent) model of the thermal contact resistance between the impacting droplet and the substrate is also incorporated in the formulation. The numerical model is solved using a Galerkin finite element method, where a deforming, adaptive triangular-element mesh is employed to accurately simulate the large-domain deformations caused by the spreading and recoiling of the impinging droplet fluid. The experimental work has been conducted in reduced gravity in the range 2×10 −4 to 5 ×10 −4 g with technically relevant impact velocities of ∼0.2 m/s, in order to provide validation of the numerical 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 results in terms of the Froude and the Ohnesorge numbers aids their interpretation. Among the results that stand out is the formation of a large number of frozen ripples on the droplet surface as a result of the simultaneous manifestation of rapid fluid oscillations and solidification. Furthermore, a non-intuitive behavior of the solidification times is reported. Specifically, the dependence of the solidification time on the Froude number is not monotonic, but features a minimum for each distinct value of Ohnesorge number considered in this study. Despite the complexity of the phenomena, the numerical 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.