# Magnetic Nanofluid Droplet Impact on an AAO Surface with a Magnetic Field
## 1 Introduction  
The dynamic behavior of droplets impacting solid surfaces has always been an attractive issue in interface impact studies due to its wide range of applications. In general, the dynamic behavior can be divided into several kinds of types, such as deposition, sticky vibrating, prompt splash, corona splash, receding break-up, partial rebound, and complete rebound [1; 2]. Many studies have shown interest in various parameters, such as contact time, bouncing off surface, bouncing height, rebound number, deposition, and spreading diameter. Different parameters of the impact droplet dominate the corresponding application areas. For example, the effect of a shorter contact time or bouncing off surface is an important consideration in anti-icing [3] and self-cleaning [4] applications, which are able to prevent water or dust from adhering to surfaces. On the contrary, in spray cooling [5], a longer contact time or deposition can keep the water on the surface and further enhance the heat removal efficiency. In order to reduce the amount of materials used in spray coating and painting [6], the maximum spreading diameter is an parameter of interest. It is also particularly important in other applications, like plasma spraying [7], pharmaceutical industry [8], ink-jet printing [9], metal forming [10; 11], and combustion [12; 13]. In 1876, [PERSON] was first drawn to an interesting phenomenon of milk or mercury droplet impact on a smoked glass plate, showing the complex shapes [14]. It was revealed that the droplet separation and elongation increases when the height of the fall is increased. In general, when a droplet is impacting on a solid surface, the deformation of the droplet is affected by the properties of the liquid (impact velocity, size, density, surface tension, viscosity, etc.) and solid surface (morphology, roughness, adhesion force, etc.). Some parameters are usually expressed by two dimensionless numbers, the Webernumber (We) and the Reynolds number (Re). Here, We \(=\rho V_{0}{}^{2}\mathrm{d}_{0}/\sigma\) characterizes the ratio of kinetic energy to the surface energy and \(\mathrm{Re}~{}=\rho V_{0}\mathrm{d}_{0}/\upmu\) describes the ratio of inertial forces to viscous forces, where \(\rho\) is the density of liquid droplets; \(V_{0}\) and \(\mathrm{d}_{0}\) are the droplet initial impact velocity and diameter, respectively; \(\sigma\) is the surface tension of liquid droplets; and \(\upmu\) is the viscosity of liquid droplets. [PERSON] et al. [15] reported an experimental study on the impact force of different droplets colliding with a flat polished aluminum plate. The dimensionless impact force is independent of the Weber number in the range of \(68<\mathrm{We}<858\), but changes with the Reynolds number. The change in surface tension has little effect on peak force in the range of \(68<\mathrm{We}<858\). In the viscosity-dominated zone (\(2.9<\mathrm{Re}<20\)), the effect of viscosity plays an important role in dimensionless impact force. [PERSON] and [PERSON] [16] developed an analytical model for predicting the dimensionless maximum spreading diameter (the maximum spreading diameter normalized in terms of initial droplet diameter). On the other hand, some studies have focused on examining the droplet impact under different surface conditions. An experimental study on the spreading of water droplets impinging on the rough surface was conducted by [PERSON] et al. [17]. The texture pattern of the substrate may make the spreading pattern of an impacting droplet spread asymmetrically and further lead the liquid to splash. [PERSON] et al. [18] showed that the pillared surfaces with a larger apex angle could induce larger robust pancake bouncing. [PERSON] et al. [19] introduced the impact dynamics of a microliter water droplet on a micropillared hydrophobic surface with different pitch of the pillars. Increased spacing of pillars will result in different bouncing regimes (from non-bouncing to complete bouncing, to partial bouncing, then back to non-bouncing). [PERSON] et al.