**5. Fragment size and distribution**

Drop size in atomization is a key parameter that is needed for a lot of fundamental researches and applications [87]. Due to the complicated nature of atomization, most nozzles cannot produce sprays of uniform droplet size. Instead, the spray can be regarded as a spectrum of drop sizes distributed about some defined mean drop size. Now, the most widely used mean diameter is Sauter mean diameter,

$$D\_{32} \text{ or } \text{SMD} = \frac{\sum n\_i d\_i^3}{\sum n\_i d\_i^2} \tag{19}$$

where *ni* is the number of droplets per unit volume in size class *i*, and *di* is the droplet diameter [7, 88–91].

The liquid in prefilming air-blast nozzle is first spread into a very thin sheet or film, which is then exposed to gas operating at the high velocity causing breakup and atomization. By spreading bulk liquid into film, contact area between liquid and gas increases. Generally speaking, SMD will decrease with the increase of gas velocity. However, under some conditions of prefilming atomization, the droplet size increases with the increase of gas velocity, and then decreases with the increase of gas velocity. So, the classical KH-RT atomization model [92–94] is modified and extended to the prefilming air-blast atomization [95].

Droplet size distribution is a crucial parameter of atomization process besides droplet mean diameter. Atomization and spray presents a wide distribution of fragment sizes. Many empirical relationships have been proposed to characterize the distribution of droplet sizes in atomization, for example, Rosin-Rammler, Nukiyama-Tanasawa, log-normal, root-normal, and log-hyperbolic. Atomization process involves a succession of changes of liquid topology, the last being the elongation and capillary breakup of ligaments torn off from the liquid surface. Breakup of liquid ligament (filament or fiber) is the key in primary atomization and secondary atomization, so ligament-mediated spray formation model is proposed [96, 97]. Drop fragments after ligament breakup is found to be gamma distribution. Then, the broad statistics of atomization shows Marshall-Palmer exponential shape of overall distribution in spray [98–101].

## **6. Complex fluids**

Complex fluids are mixtures that have a coexistence between two or multiphases, which are common in our society and industry [102–104]. Many complex fluids are non-Newtonian fluid, whose characteristics of breakup and atomization are unusual [82, 105–107].

approximately. So the theoretical criterion *NRT* could be the new criterion instead of

<sup>þ</sup> *<sup>C</sup> Oh*<sup>2</sup> *Wec* !<sup>1</sup>*=*<sup>3</sup>

¼ 1*,* (18)

When the viscosity of liquid cannot be neglected, *Oh* will be another key parameter [79–84]. Many researches show that the *We* range of drop breakup mode will increase with the increase of *Oh* nonlinearly. The most important transition *We* is the critical Weber number *Wec* occurring at the start of bag breakup. It can establish the criteria for the onset of secondary atomization. Based on the RT

*We* in the range of general bag breakup as shown in **Figure 3**.

*Environmental Impact of Aviation and Sustainable Solutions*

*Theoretical criterion NRT for general bag breakup.*

**Figure 3.**

**Figure 4.**

**78**

*Drop interaction regime map.*

instability, the theoretical formula for predicting *Wec* is [81]

*We*<sup>0</sup> *Wec* � �<sup>1</sup>*=*<sup>2</sup>

The particle concentration in the pinch-off zone of suspension or slurry decreases as its minimal diameter decreases, resulting in a pure liquid interstitial fluid. There are three successive stages during suspension pinch-off, referred to as suspension, transition, and liquid stages, which is different from pure liquids [108–111].

*ωkm=ωRm* ¼ 1*:* (20)

Atomization of viscoelastic liquids is widely known to be more difficult to atomize than typical Newtonian liquids [18, 132–138]. The addition of viscoelasticity is found to stabilize the rim of liquid. Viscoelasticity can enhance the growth of the bead and delay pinch off. Viscoelasticity increases the mean drop diameter and broadens the size distribution. Liquids with atypical properties, such as gels, liquid

The available literature on liquid atomization is countless. Many researchers and engineers have done a lot of excellent work in this field. Unfortunately, the clear physical mechanisms on atomization have not yet been fully revealed. Some topics have received only cursory attention, such as non-Newtonian liquids, charged liquids, and turbulence influence. There are many challenges ahead for research in atomization and spray technology [148, 149]. On the other hand, it is lucky for us. Due to the fundamental nature of the problem and its many important applications, we can expect great progress in the fields of atomization and spray technology in

This work was supported by the National Key R&D Program of China (2018YFC0808502-02), National Natural Science Foundation of China (21506059), Shanghai Engineering Research Center of Coal Gasification (18DZ2283900), and

Key Laboratory of Coal Gasification and Energy Chemical Engineering of Ministry of Education, Shanghai Engineering Research Center of Coal Gasification, East China University of Science and Technology, Shanghai, People's Republic of China

© 2019 The Author(s). Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/ by/3.0), which permits unrestricted use, distribution, and reproduction in any medium,

Fundamental Research Funds for the Central Universities.

\*Address all correspondence to: hfliu@ecust.edu.cn

provided the original work is properly cited.

The authors have declared that no conflict of interest exists.

metal, and strain-thickening liquids, are also studied widely [139–147].

*Breakup Morphology and Mechanisms of Liquid Atomization*

*DOI: http://dx.doi.org/10.5772/intechopen.84998*

**7. Conclusions**

the future.

**Acknowledgements**

**Conflict of interest**

**Author details**

**81**

Hui Zhao and Haifeng Liu\*

For evaluating the breakup of non-Newtonian fluid, the mean apparent viscosity of liquid during deformation and breakage is the key parameter. Three methods for determining the apparent viscosity of non-Newtonian fluid have been presented: (1) calculation of mean apparent viscosity according to the shear rate equal to *γ* ¼ *ug=D* [112], (2) increase the constant *k* determined by other test parameters, *γ* ¼ *kug=D* [17, 113], and (3) numerical analysis or analytical solution of energy and motion equations to determine dynamic shear rate [114–117].

Based on morphology, the breakup regimes of slurry jet can be classified into different modes: Rayleigh-type breakup, fiber-type breakup, superpulsating breakup, and atomization [113, 118, 119]. The particles in slurry will make membrane breakup very fast, so the membrane structure is not obvious in slurry atomization as shown in **Figure 5**. The dimensionless slurry jet breakup length can be correlated by the KH-RT hybrid model [92, 93, 113, 120]. There are two kinds of periodic structures, which are shear wave and jet oscillation. The deformation and breakup regimes of slurry drops can be classified into different modes: deformation, multimode breakup (including two submodes: hole breakup and tensile breakup), and shear breakup [17, 117].

Atomization of solution is a common phenomenon in numerous practical applications [121–124]. In the breakup of surfactant-laden liquid, critical micelle concentration (CMC) has an important influence [125–129]. The micelle can be considered as the source term, which can supply the monomers [130]. The diffusion rate of surfactant is limited, and liquid breakup is very fast sometimes. So, dynamic surface tension will change with the process of liquid deformation and atomization. According to the competition of the amplification rate of KH instability *ωkm* and RT instability *ωRm*, the criterion on transition Weber number between general bag breakup and shear breakup is obtained [131],

**Figure 5.** *The breakup regimes of slurry jet.*

*Breakup Morphology and Mechanisms of Liquid Atomization DOI: http://dx.doi.org/10.5772/intechopen.84998*

$$
\alpha\_{km}/\alpha\_{Rm} = \mathbf{1}.\tag{20}
$$

Atomization of viscoelastic liquids is widely known to be more difficult to atomize than typical Newtonian liquids [18, 132–138]. The addition of viscoelasticity is found to stabilize the rim of liquid. Viscoelasticity can enhance the growth of the bead and delay pinch off. Viscoelasticity increases the mean drop diameter and broadens the size distribution. Liquids with atypical properties, such as gels, liquid metal, and strain-thickening liquids, are also studied widely [139–147].
