Introductory Chapter: Droplet Formation and Evolution

1. Introduction

Nowadays, decreasing carbon emissions becomes the global consensus. Therefore, in order to achieve carbon neutrality in the near future, many efforts should be done including energy transition, carbon capture, and carbon utilization. Among them, liquid-droplet flow can be applied in many industries, such as the internal combustion engine, colling machines, coating machines, hydraulic transmission equipment agricultural irrigation, and oil-gas transportation.

2. Liquid droplet formation

Generally, nozzles or orifices are often applied to disperse the liquid into the air environment or another immiscible liquid. The discrete droplet is called the discrete phase, while the gas or other liquid is called the continuous phase. In addition, during the liquid-gas interaction, the liquid film may still break into small droplets. Therefore, in the industrial field, especially in the field of internal combustion engines, the discrete phase and continuous phase fluids move together, finally forming a common two-phase (gas-liquid) fluid. For example, the liquid fuel is firstly injected into the cylinder and atomized by the air movement. After fully mixed with air, fuel droplets are ignited and then explosively burned. The main mechanical behaviors of droplets are shown as follows:

1. “Internal circulating flow”—The shear force generated by the friction between the two phases in the continuous phase fluid causes the droplets to flow, called internal circulating flow.

2. “Deformation”—Small droplets are spherical, while large droplets tend to deform and eventually become ellipsoids due to uneven pressure distribution on the droplet surface.

3. “Oscillation”—When the Reynolds number of the droplet is large, the behavior of surface vibration and even vibration deformation will occur, called oscillation.

4. “Breakup”—The droplet itself breaks into several droplets, or multiple droplets collide and then break into several droplets.

5. “Coalescence”—When the droplets collide with each other, they merge into larger droplets due to viscous forces.

3. Impingement and evaporation

After droplet formation, it moves forward and may impact the solid wall or other phase, some behaviors then can be involved as shown in Figure 1.

1. “Stick”—in which the impinging droplet adheres to the wall in nearly spherical form. This occurs when the impact energy is very low and the wall temperature T_w is below T_PA (pure adhesion temperature, below it adhesion occurs at low impact energy).

2. “Spread”—where the droplet impacts with a moderate velocity onto a dry or wetted wall and spreads out to form a wall film for a drywall, or merges with the pre-existing liquid film for a wetted wall.

3. “Rebound”—in which the impinging droplet bounces off the wall after impact. This regime is observed for two cases: (a) on a drywall when T_w ≥ T_PR, (pure rebound temperature, above which bounce occurs at low impact energy), in this case, contact between the liquid droplet and the hot surface is prevented by the intervening vapor film; (b) on a wetted wall, when the impact energy is low, and the air film trapped between the droplet and the liquid film causes low energy loss and results in bouncing.

4. “Rebound with breakup”—where the droplet bounces off a hot surface (T_w < T_PR), accompanied by break up into two or three droplets.

5. “Boiling-induced breakup”—in which the droplet, even at very low collision energy, disintegrates due to rapid liquid boiling on a hot wall whose temperature lies near the Nakayama temperature T_N (is the Nakayama temperature at which a droplet reaches its maximum evaporation rate).

6. “Breakup”—where the droplet first undergoes a large deformation to form a radial film on the ‘hot’ surface (T_w > T_PA), then the thermo-induced instability within the film causes the fragmentation of the liquid film in a random manner.

7. “Splash”—in which, following the collision of a droplet with a surface at very high impact energy, a crown is formed, jets develop on the periphery of the crown and the jets become unstable and break up into many fragments.

Figure 1.

Droplet impacting behaviors.

The existence of these impingement behaviors is governed by a number of parameters characterizing the impingement conditions. These include incident droplet velocity, size, temperature, incidence angle, fluid properties such as viscosity, surface tension, wall temperature, surface roughness, and if present wall film thickness and gas boundary layer characteristics in the near-wall region. Quantitative criteria for the behavior transitions from Bai and Gosman [1] and refined in the present work are presented in Figure 2.

Figure 2.

Behavior transition conditions.

All these droplet behavior including formation, evaporation, and evolution should be clarified to clearly understand the droplet dynamic. Especially for the current “carbon cycle” age, all the equipment should be re-design or developed with less CO₂ emission to protect local environments. Among them, the droplets dynamic can be applied in many new technologies or even develop future renewable fuels.

Acknowledgments

The author would like to acknowledge the National Natural Science Foundation of China [Grant 51909037] and the Foundation of State Key Laboratory of Engines [No. K2022-12].

Conflict of interest

The authors declare no conflict of interest.