A numerical study of the coalescence of hollow droplets under solidification

Abstract

This paper presents the results of numerical simulations of the coalescence and solidification of two hollow droplets. A base droplet (i.e., a pre-solidified droplet) stays on a supercool surface that causes its shell liquid to solidify. An incoming droplet then flows toward and coalesces with the base droplet. After coalescence of the droplets, the two hollow cores can coalesce depending on the momentum of the incoming hollow core and the solidification rate. A high solidification rate corresponding to a high Stefan number St prevents the hollow cores from coalescing and thus induces a discrete hollow-core solidified product, whereas a low St number results in a coalesced hollow-core (CH) droplet. However, the coalescence of two droplets and/or their hollow cores does not affect the apex at the top of the final solidified droplet, which is created by volume expansion upon phase change. Some other parameters including the Peclet number Pe, the Weber number We, the size Ris of the incoming inner core, the position Hs of the incoming droplet and the number of cores Ni of the incoming droplet also affect the coalescence and phase transition of the droplets. It is found that transition from a CH region to a discrete hollow-core region occurs for lower Pe, Ris, or Ni. In contrast, decreasing the value of We or Hs enhances the CH region. Moreover, we provide regime diagrams based on the supercooling degree, the Peclet number, and the size of the inner core of the incoming droplet.