Scale analysis of undercut and bulge driven by thermocapillary convection due to surface-active solute on a solidified surface

This study scales the shape of the undercut, a depression region near the triple-phase line parallel to the scanning direction, and the bulge in the central region within the fusion zone, considering thermocapillary convection affected by a surface-active solute in the molten pool for the first time. Undercuts, commonly encountered in welding, additive manufacturing, and re-solidification processes, reduce fatigue and fracture strength while enhancing stress concentration. Utilizing the interfacial Young–Laplace equation and Bernoulli equations in the shear layer driven by thermocapillary force influenced by the surface-active solute-affected critical temperature, and introducing the concept of mass conservation, the scale analysis finds that the undercut depth and bulge height increase as Marangoni and Prandtl numbers increase, and the loss coefficient decreases. Furthermore, the widths of the undercut and bulge exhibit increases with dimensionless beam power, fusion zone width, and the ratio of solid-to-liquid thermal conductivity. The COMSOL Multiphase code is also used for simulation and successful comparison, aligning with experimental data from laser polishing. This analysis aids in understanding and controlling microstructures in various processes beyond laser polishing.