Numerical study of a hollow pileup yielded by deposition of successive hollow droplets

Abstract

Understanding the pileup formation process of sequentially deposited droplets is vital in advancing droplet-based printing technologies. While pileups of simple droplets have been extensively studied, knowledge of the hollow pileup formation is inadequate. This paper presents a fully resolved numerical analysis of the pileup formed by successively depositing incoming hollow droplets on a pre-solidified (or base) droplet on a supercool surface. An axisymmetric front-tracking method is used to handle the simulations. The pileup height increases as the incoming droplets coalesce, while the hollow cores may or may not merge. The pileup shape and its hollow configuration depend on parameters such as the Stefan number, Peclet number, Weber number, Fourier number, and the size and number of hollow cores. Varying these parameters does not affect the peak formation at the top of the pile caused by volume expansion during phase change, although the Fourier number has a strong influence on the mean aspect ratio and solidification time of the pileup. Increasing the deposition rate enhances the coalescence of hollow cores and reduces the mean aspect ratio of the pileup. Reducing the Stefan number also promotes hollow core coalescence, which decreases the mean aspect ratio. However, the size of the hollow core and the Peclet and Weber numbers have almost no influence on the outer shape of the hollow pileup. The effect of the number of incoming droplets on the pileup formation is also revealed.