Numerical simulation of liquid droplet solidification on substrates

A mathematical model describing the deformation and solidification behavior of liquid droplets impinging on substrates is presented. The mathematical model is numerically solved using a finite element method. In the experiment, a molten tin droplet (2.2-4.3 mm diameter) impacts copper, stainless steel and glass substrates at various preimpact velocities (1.4-4.0 m/s). The values of the heat transfer coefficient at the droplet/substrate interface are evaluated by comparing the calculated splat diameters to the experimental ones. The estimated values are within the previously reported ranges. The model almost predicts the Weber number dependence of the experimental splat diameters. The time variations of the numerical splat diameters also agree with the experimental results. The simulation reveals that the frozen layer at the splat edge, rather than at the center region, affects deceleration of the droplet spreading. The effect of the solidification on the splat diameter is explained from the freezing rate at the splat edge.