## 1 Introduction  
Nanofluid fuels are a novel type of supplementary fuel family, which were defined as colloidal suspensions of high energetic nanoparticles in liquid fuels [1]. Their combustion characteristics have been widely investigated, indicating high energy density [2; 3], ignition probability [4], combustion efficiency [5; 6], and low pollutant emissions, etc. [7; 8]. Atomization is an imperative and crucial step to improve the combustion performance of nanofluid fuels. The electrostatic atomization is a liquid fuel atomization technique relying solely on electrical charging and has been widely investigated [9; 10]. It is of ever-increasing importance in an extensive range of industrial and scientific processes as it is in principle suitable to a variety of technological applications [11; 12]. The secondary breakup of droplets is an important segment for atomization. The importance of secondary breakup of nanofluid fuel droplets lies in distributing nanomaterialsin each droplet to make the subsequent combustion step more efficient, and possibly reducing the effect and probability of agglomeration on compaction and sintering. This triggers our motivation to investigate the characteristics of the secondary breakup of nanofluid fuel droplets and deeply recognize the process and mechanism. Electrostatic atomization of pure liquid fuel has been widely investigated, and the mechanism shows that the electrification and the physical properties are crucial to produce excellent breakup performance. As the electric field force is greater than the surface tension, the pure droplet will coulombically break up [13; 14]. For binary or trinary mixtures adding necessary additives, due to the changes of physical properties like the surface tension, viscosity, and density, the atomization performance is significantly influenced. [PERSON] et al. [15] reported that the viscosity has a contribution of \(\sim\)90% to lead to the change in Sauter mean diameter (SMD), whereas the density causes only less than 2% change. For nanofluid fuels, their physical properties are significantly different from host liquid fuel [16; 17]. Herein, the key point is that the change in the physical properties of nanofluid fuels containing different nanoparticle concentrations can potentially alter the atomization characteristics. Besides physical properties, electric field conditions are crucial to influence atomization performance. The electrostatic atomization performance of nanofluid fuel mainly depends on: (1) Nanoparticles; nanoparticles can change the physical properties of the original base fuel, including thermal conductivity, heat transfer coefficient [18; 19], density, viscosity, conductivity, and surface tension, etc. [16; 17]. Our previous work demonstrated that Al nanoparticle concentration had a significant effect on the physical properties of Al/n-decane nanofluid fuel [20]. Such changes in the physical properties will result in a corresponding change in the gravity, surface tension, viscous force, and electric field force to influence the electrostatic breakup performance of nanofluid fuel. (2) Charging; in the electrostatic field, nanofluid fuel droplets will be subjected to the combined action of gravity, surface tension, viscous forces, and electric field force. When the electrical force overcomes the surface tension, the droplet will be disintegrated [21; 22]. Electrical force can exist only if the charge is present, and the value of electrical force is proportional to the charge in a uniform electrostatic field. The charge of droplets will affect the breakup mode and the size of breakup droplets. The literature has shown the key factors influencing the secondary breakup characteristics of pure liquid fuel, including the surface tension, charge-to-mass ratio, droplet size, but the impact of adding nanoparticles on the secondary breakup of the host liquid has been scarcely reported.