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In the drop-on-demand 3D printing technique, molten drop impact is crucial to the understanding of the formation of the building block of a part. However, existing studies cast less due attention to the rebounding dynamics of molten drops. This paper thus develops a phase field method to that end. The model consists of the Cahn-Hilliard equation, coupled with the Navier-Stokes equation to track the evolving liquid-gas interface. A heat source is added to the energy balance equation to distinguish between solid and fluid. The model is discretized using a finite difference method on a semi-staggered grid, and is paralleled based on the shared memory parallelism, OpenMP. The model was first compared with an experiment before being applied to various impacts. The agreement is reasonable. Typical impacts in 3D printing conditions were considered. The major findings are that the Tin drop rebounds off the substrate with a dimpled bottom when the impact velocity is 1 m/s, but with a rounded one when the impact velocity is reduced by half, and that the dimpled bottom is caused by an entrapped bubble during the receding process. Besides, effect of solidification on drop rebounding was examined as well. [ABSTRACT FROM AUTHOR]

• A free-energy-based surface tension model used in the conservative level set modeling. • Distinct impact regimes in 3D printing conditions considered. • Parallel computing based on OpenMP employed. The recently developed conservative level set method is second order in nature, thus making it amenable to explicit finite difference solutions in three dimensions. Due to a lack of efficient numerical models in simulating impact-freezing problems in 3D printing conditions, this paper puts forward a model based on the coupling of the conservative level set equation and the Navier-Stokes equations. The interfacial tension is represented by the free-energy-based model, which is free from the cumbersome computation of curvature that may induce parasitic flows. The model is further augmented with the thermal field to deal with phase change. The model is discretized on a half-staggered grid, is written in FORTRAN, and is accelerated with the shared-memory parallelism, OpenMP. Furthermore, a simple yet effective dynamic contact angle is applied. Three validation tests were conducted, corresponding to different impacting regimes. It shows that the model could well predict the full rebounding, and especially, the splashing occurring in drop impact onto solid surfaces. [Display omitted] [ABSTRACT FROM AUTHOR]

• The solution of the Cahn-Hilliard equation to track moving boundaries. • A heat source term added in energy equation to trace solidification profile. • Thermal contact resistance studied to find its effect on maximum spread factor. • A supersonic impact of ceramic particles examined. A modified phase-field three-dimensional model has been developed to simulate the spreading of an impacting droplet undergoing solidification. The model is based on the numerical solution of the Cahn-Hilliard equation coupled with the Navier-Stokes equations for fluid flow and the energy balance equation for heat transfer. The solidification profile is tracked by treating the latent heat as a source term in the energy equation, which is modified to work with the Cahn-Hilliard equation. To verify the model, five cases were tested and matched well with experiments. Also, the effect of thermal contact resistance on the maximum spread factor of a solidifying droplet is discussed. One case was taken from practical thermal spraying conditions where a solidifying ceramic droplet spreads on a cold surface at a supersonic impact velocity; computed results are consistent with available measurements. [ABSTRACT FROM AUTHOR]

• The solution of the Cahn-Hilliard equation to track moving liquid-gas boundaries. • Drop impact under a horizontal electric field considered. • Drop splashing suppressed using electric force. A 3-D diffuse interface model has been developed to simulate impact of a dielectric droplet under the influence of a horizontal electric field. The Cahn-Hilliard equation, coupled with the Navier-Stokes equations, is employed to track liquid-gas interface. The model is discretized utilizing the finite difference method on a half staggered grid and solved using the projection method with the aid of OpenMP. Mesh independence test was also performed to choose an appropriate grid size. After validating the model, extensive simulations were conducted. The paper takes into account various factors influencing drop impact dynamics under real conditions, such as contact angle and impacting velocity. Numerical results show that for a moderate electric field, the electric force stretches a droplet in the direction of the applied electric field, and that a horizontal electric field can be useful to suppress splashing by reducing the rising angle made by the lamella with the substrate. [ABSTRACT FROM AUTHOR]

• Sequential droplet impact with grain growth and impingement is modelled. • Typical velocities of crystal growth are within 2 m/s. • Solidification time of a single splat on a stainless steel substrate is about 0.5 μs. • The undercooling in crystal growth ranges approximately from 150 K to 500 K. A coupled CFD and diffuse interface model was developed to predict the dynamic process of solidification microstructure formation of sequential yttria-stabilized zirconia (YSZ) droplet impact under supersonic plasma spraying. The numerical model relies on the explicit finite difference solution of the Navier-Stokes and energy balance equations, coupled with the Cahn-Hilliard equation, to track liquid-gas interface, and of a phase field model for solidification microstructure formation involving polycrystalline growth to trace solid-liquid interface. Extensive simulations, differing in the status of the first droplet and the impacting parameters of the second one, were carried out. The results reveal that solidification microstructure still follows a columnar pattern if the second droplet lands on the first that is just starting spreading, and that the growth direction around the contact region in the second splat will be obviously skewed by fluid flow if the first has been solidified, owing to earlier and easier nucleation on the top surface of the first splat, thus confirming the epitaxial growth across the splat-splat interface. Computed results are also compared with thermal spray experiments, with gratifying agreement obtained. [ABSTRACT FROM AUTHOR]

• The solution of the Cahn-Hilliard equation to track moving liquid-gas boundaries. • A phase field model for polycrystalline growth used to track solid-liquid interface and grain boundaries. • Supersonic YSZ droplet impact considered. • Convection effect on solidification microstructure investigated. A comprehensive numerical model has been developed, which is capable of representing the impact and spreading of a high-velocity yttria-stabilized zirconia (YSZ) molten droplet with microstructure formation in plasma thermal spraying processes. The numerical model entails the explicit finite difference solution of the Navier-Stokes equations and the energy balance equations, coupled with the Cahn-Hilliard equation to track the liquid-gas two phase interface and with a phase field model for solidification microstructure formation involving the polycrystalline growth. Numerical model procedures are given. The model, after being checked for mesh-independence, was applied to study the spreading and solidification of a high-temperature high-velocity YSZ droplet impinging upon a preheated substrate surface under the conditions typical of supersonic plasma thermal spraying processes. Extensive numerical simulations were carried out and results reveal that the solidification microstructure formed in the spreading droplet consists primarily of columnar grains. Computed results are also compared with thermal spray experiments, and gratifying agreement is obtained. [ABSTRACT FROM AUTHOR]