Phase Field Modeling of Air Entrapment in Binary Droplet Impact with Solidification Microstructure Formation
Abstract
:1. Introduction
2. Mathematical Statement
2.1. Mass, Momentum, and Energy Equations
2.2. Equation for an Evolving Gas–Liquid Interface
2.3. Solidification Microstructure Formation
2.4. Gas Compressibility
2.4.1. Compression Started Sometime before Real Contact
- A.
- Estimate of air layer thickness and of the strength of decelerationThe top of the bubble moves upwards instead of downwards after contact with the substrate, while the dimple is formed before contact with the substrate. is the air layer thickness at first contact. Assume compression begins a distance away from the substrate. Figure 2 shows the dynamics of air entrapment with various lengths involved. The time elapsed from (a) to (b) is of little interest and can be estimated to be The pressure at the bottom of the droplet in (b) can be approximated as , since it is assumed that compression begins for the first time at this height. H is a length scale comparable to H*. Subsequently, the pressure in the gas rapidly accumulates, indicating the beginning of compression.
- B.
- Estimate of and the time for the first stage of compression
2.4.2. Compression Completed When the Bubble Recedes
- A.
- How is the bubble enclosed?
- B.
- Estimate of the time for the second stage of compression
2.4.3. Gas Bubble Receding
2.5. Boundary Conditions
2.6. Numerical Procedures
3. Results and Discussion
3.1. Model Validation
3.2. Typical Binary Droplet Impact under Plasma Spraying Conditions
3.3. Effect of Droplet Porosity
3.4. Sequential Droplet Impact with Well Bonding
4. Concluding Remarks
- When two droplets—initially separated by less than the maximum spread diameter as if one droplet impinged—impact simultaneously onto a solid surface, air would be trapped near the spread front and the grain boundary nearby curved towards the liquid.
- If one of the droplets is hollow, then air entrapment may not take place near the spreading front, since the liquid jet of higher kinetic energy—obviously from the dense droplet—when coming close to the less energetic one, may push the oncoming liquid backwards, thus leaving a concave surface on the splat formed by the hollow droplet.
- Air entrapment can be eliminated if the second droplet is introduced when the first is completely solidified. In the parameters used herein, the horizontal distance between the two droplets should be around 90% of the maximum spread diameter as if one droplet impacted.
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
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Shen, M.; Li, B.Q. Phase Field Modeling of Air Entrapment in Binary Droplet Impact with Solidification Microstructure Formation. Coatings 2022, 12, 1990. https://0-doi-org.brum.beds.ac.uk/10.3390/coatings12121990
Shen M, Li BQ. Phase Field Modeling of Air Entrapment in Binary Droplet Impact with Solidification Microstructure Formation. Coatings. 2022; 12(12):1990. https://0-doi-org.brum.beds.ac.uk/10.3390/coatings12121990
Chicago/Turabian StyleShen, Mingguang, and Ben Q. Li. 2022. "Phase Field Modeling of Air Entrapment in Binary Droplet Impact with Solidification Microstructure Formation" Coatings 12, no. 12: 1990. https://0-doi-org.brum.beds.ac.uk/10.3390/coatings12121990