# Symmetry-Breaking-Induced Internal Mixing Enhancement of Droplet Collision

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## Abstract

**:**

## 1. Introduction

## 2. Symmetric Collision between Two Identical Droplets

## 3. Symmetry-Preserving Methods for Binary Droplet Collision

## 4. Symmetry Breaking between Two Droplets of Unequal Sizes

## 5. Collision between Two Different Droplets

## 6. Internal Mixing Enhancement by Non-Newtonian Effects

## 7. Spin Effects on Droplet Collision and Internal Mixing

## 8. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 1.**Schematic of the symmetric characteristics between two identical droplets undergoing the (

**a**) head-on collision and the (

**b**) off-center collision.

**Figure 2.**Experimental images of three distinct collision outcomes (bouncing, coalescence, and separation) [4] showing the (

**a**) axisymmetry and mirror symmetry for the head-on collision and the (

**b**) rotational symmetry for the off-center collision. Adapted with permission from Jiang et al. [4] Copyright 2006, Cambridge University Press.

**Figure 3.**Schematic of the numerical symmetry-preserving setting for the (

**a**) head-on collision and the (

**b**) off-center collision.

**Figure 4.**Experimental images of the collision between two droplets of unequal sizes. (

**a**) the pinch-off phenomenon of water droplets (adapted with permission from Zhang et al. [75] Copyright 2009, American Physical Society), (

**b**) three distinct collision outcomes of tetradecane droplets (adapted with permission from Tang et al. [24] Copyright 2012, American Institute of Physics), and (

**c**) the mushroom-like internal jet structures of water droplets (adapted with permission from Tang et al. [49] Copyright 2016, Cambridge University Press).

**Figure 5.**Experimental images of the collision between two droplets of different fluids. (

**a**) reflexive separation between diesel and ethanol droplets (adapted with permission from Chen [76] Copyright 2006, Elsevier Ltd.), (

**b**) coalescence between a high viscous droplet and a low viscous droplet (adapted with permission from Focke et al. [83] Copyright 2013, Elsevier Ltd.), (

**c**) coalescence between ethanol and water droplets (adapted with permission from Gao et al. [78] Copyright 2005, Springer-Verlag), (

**d**) coalescence between methanol and hexadecane droplets (adapted with permission from Wang et al. [88] Copyright 2004, The Combustion Institute), and (

**e**) termed “crossing separation” between glycerol solution and silicon oil droplets (adapted with permission from Planchette et al. [79] Copyright 2012, Cambridge University Press).

**Figure 6.**Numerical simulation results of the head-on collision between two non-Newtonian droplets. (

**a**) two different shear-thinning fluids; (

**b**) two identical shear-thickening droplets; (

**c**) one shear-thinning droplet (lower) and another shear-thickening droplet (upper). Adapted with permission from Sun et al. [67] Copyright 2015, American Physical Society.

**Figure 7.**The collision between two spinning droplets. (

**a**) droplet deformation for the bouncing and separation between two spinning droplets, (

**b**) schematic of the conservation of angular momentum for the arbitrary off-center droplet collision, and (

**c**) evolution of the temporal contact surface area to characterize the internal mixing affected by droplet spinning effects. Adapted with permission from He and Zhang [68] Copyright 2020, American Physical Society.

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**MDPI and ACS Style**

Leng, Y.; He, C.; Wang, Q.; He, Z.; Simms, N.; Zhang, P.
Symmetry-Breaking-Induced Internal Mixing Enhancement of Droplet Collision. *Symmetry* **2024**, *16*, 47.
https://doi.org/10.3390/sym16010047

**AMA Style**

Leng Y, He C, Wang Q, He Z, Simms N, Zhang P.
Symmetry-Breaking-Induced Internal Mixing Enhancement of Droplet Collision. *Symmetry*. 2024; 16(1):47.
https://doi.org/10.3390/sym16010047

**Chicago/Turabian Style**

Leng, Yupeng, Chengming He, Qian Wang, Zhixia He, Nigel Simms, and Peng Zhang.
2024. "Symmetry-Breaking-Induced Internal Mixing Enhancement of Droplet Collision" *Symmetry* 16, no. 1: 47.
https://doi.org/10.3390/sym16010047