Molten droplet deposition and solidification at low Weber numbers

Low Weber number deposition of small molten droplets on cold targets is of importance in certain dropwise buildup processes, but at this time, critical elements are absent from our theoretical understanding of the deposition process, and prediction from basic principles is not possible. This paper lays down a framework for understanding low Weber number deposition in terms of similarity laws and experimentation. Based on experiments from the highly viscous limit to the inertia-dominated limit, correlations are given for the spreading velocity, spreading time scales, post-spreading oscillation amplitudes, and oscillation damping time scales. Molten droplets are arrested, and their final solid shape determined, by contact line freezing. In homologous deposition, where the drop and the target are of the same material, the spreading factor is determined principally by the Stefan number, the dimensionless parameter which measures the temperature difference between the fusion point and the target temperature. Some concluding remarks are offered on what needs to be done to accurately compute such deposition processes.