# Numerical Investigation of Air Entrapment Dynamics for High-Speed Thermal Spraying
## 1 Introduction  
Droplet impacts on an impermeable surface is a common phenomenon and used in many applications, such as pesticide spraying, spray coating, and inkjet printing. After the liquid droplet impacts the solid surface, it may spread, splash, break up, recoil, or even rebound, depending on the initial impacting conditions [1], the characteristics of the droplet [2], and the substrate [3, 4]. Interestingly, air entrapment can always be discovered, no matter how the droplet behaves, which could critically affect its spreading process and outcome [5]. For thermal spray applications, entrapped air is particularly undesired, as this would leave pores in the coating and significantly lower the quality of the splat-substrate adhesion [6]. Air entrapment was first discovered by [PERSON] and [PERSON] [7] during their experiment of an n-heptane droplet impacting on a stainless-steel surface. Since then, air entrapments have been widely studied, both experimentally [8, 9, 10] and numerically [11, 12, 13]. Studies on the air entrapment dynamics during thermal spraying are even harder, as the molten droplets are mostly metals and ceramics, which are opaque, making them impossible to directly observe through conventional instruments. [PERSON] [14] found many of nanopores under the nickel splat after it impacts the copper substrate with a velocity of 65 m/s, and attributed these pores to the nucleation of gas bubbles during rapid postimpact depressurization. [PERSON] [15] observed the air retention in the center of a molten molybdenum droplet impacts on analuminum substrate, and proposed that the initial contact of the molten droplet with the substrate is not a point but an annular area. Moreover, the phase transition of the molten droplet makes the theoretical model much more complicated and brings challenges to the numerical studies. There have been continual numerical modeling efforts to investigate this problem. [PERSON] [16] observed the formation of a bubble around the center in their modeling of a molten nickel droplet impacting on a flat stainless-steel surface with a speed of 50 m/s. [PERSON] [15] attributed their model's sudden temperature drop at the droplet/substrate surface to air entrapment. [PERSON] [17] developed a model by 3D Lattice Boltzmann method to investigate the air entrapment of a molten droplet impacting and solidifying on a cold smooth substrate. Depending on the contact angle of the substrate, bubbles would either be entrapped as a single air bubble or as multiple isolated bubbles. [PERSON] et al. [18] simulated the dynamics of air entrapment of a molten molybdenum droplet impacting on a flat aluminum substrate by volume of fluid (VOF) method and showed that wall heat flux had a strong relation to the dynamic features of the entrapped air film. However, these reported numerical models mainly focus on the air layer entrapped just after the molten droplet impacts the substrate, which resembles the water droplet impaction and could only explain the observed globular pores around the impact center of the finally solidified splat. However, according to the characterization of the plasma-sprayed Zirconia coating [19], pores could be found around the center and the splat periphery. [PERSON] [20] once discovered air entrapment at the moving front of a millimeter-sized tin particle landing on a flat stainless-steel surface with high impacting speeds of 100 m/s and 400 m/s in their model, but the entrapped bubbles are forced outwards during the spreading process. [PERSON] [21] also observed air entrapment along the interface during their simulations of a molten nickel droplet impacting on a stainless-steel substrate, but ascribed the bubble formation to the gas supersaturation inside the molten droplet without any further analysis. The reason for the air entrapment near the edge of the splat is still unclear. In this paper, the dynamics of the air entrapment process of a molten nickel droplet impacting on a cold smooth stainless-steel substrate is investigated.