Molten droplet deposition and solidification at low Weber numbers

Abstract

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.

Modeling the early stages of reactive wetting

“…It is interesting to note that for values of λ Re * < 0.1, no oscillatory motion was seen in the work by Ding and Spelt [19]. In Schiaffino and Sorin [18] it is experimentally determined that the transition between under-damped oscillations to over-damped decay (no oscillations) occurs as Oh increases above 1 × 10…”

“…Characteristic inertial effects, such as triple-line position oscillations and large droplet curvature variations, are reduced for Oh > 0.01 and eliminated for Oh > 1 [18].…”

“…The slip length is found by Ding and Spelt to influence the onset of oscillations that occur when the droplet transitions from the inertial stage to the diffusive stage. The critical value of Re * for which oscillations occur is reduced with decreasing λ. Hocking and Davis [21] have demonstrated that there is no simple relationship between contact angle and velocity when the approach to equilibrium becomes oscillatory, which seems to be the case in a number of experimental and numerical studies of millimeter-sized droplets [8,9,18,19].…”

Ink‐Jet Printing of Wax‐Based Alumina Suspensions

“…1); hence, the fraction that solidifies during impact may have a much stronger influence on droplet spreading. This condition has been considered by Schiaffino and Sonin, 18 who produced dimensionless analytical expressions to calculate the ratio between droplet spreading and solidification time. They found that, although the solidification time of a droplet 25-100 m in size was several orders of magnitude greater than the time taken to reach maximum spreading diameter, this diameter was controlled by solidification of the contact line.…”

Utilising inkjet printed paraffin wax for cell patterning applications

“…The final shape and surface texture of the resultant printed structure was dependent on conditions that include the wettability of the substrate and its temperature, print head temperature, gap distance from the print head to the substrate and droplet material [34][35][36] . The scalloping behaviour was due to the droplets being cooled quicker than optimal during jetted flight, after landing on the substrate, merging with the previous deposited droplet and partially retained their individual rounded contact lines [37] . Printing wax allowed the creation of a range of different complexities and channel widths that allowed the creation of thick impermeable blocks, to channels as small as 30 µm.…”