## 1 Introduction
However, in the actual 3D printing scene, droplet spreading occurs on micron-sized droplets and micron-sized powder particle systems. The spreading behaviors learned from the experimental observation [32; 33] of millimeter-sized drops cannot be completely applied to the droplets in micron size because the droplets' dynamics are size sensitive. Although the modern/advanced high-speed camera can capture ultra-fast fluid phenomenon over million frames, however, for a typical 3D printing scene, it is a big challenge to capture the images of a microdroplet (diameter < 200 \(\upmu\)m) with relative high velocity (above 1.0 m\(\cdot\)s\({}^{-1}\)) to study the spreading behaviors under the space limitation of the print head to powder bed. Limited by the experimental equipment, there is extremely inadequate research [34] on the impact of the millimeter-sized droplets on granular materials with a direct observation-based experimental method. A variety of liquid droplet impact-related simulation [35; 36; 37; 38; 39; 40] studies have been conducted to solve application problems in 3D printing. However, most existing simulation studies have focused on the effect of binder drop properties (such as surface tension and viscous force and impact velocity) on droplet spreading behaviors rather than on the physical and dynamic characteristics of the binder/powder interaction system. Therefore, the computational fluid dynamics (CFD) method used to study droplets impacting the powder surface was proposed. This study aims to develop a reliable and effective model to investigate the behavior of micron-sized droplets impacting on a micron-sized powder bed applied to the 3D printing process. First of all, referring to the previous studies and practical experience in 3D printing, we proposed a low impulse model supported by the theoretical calculation results and typical studies. Depending on this strategy, we have simplified the model of a microdroplet spreading on the well-compacted and smoothed micro-particle powder to the model of a single droplet spreading on the rigid multi-sphere substrate, which matches well with the actual 3D printing process. Then, the CFD model for numerical simulation based on the VOF (volume of fluid) method was established. In order to test the VOF model proposed in this study, the observation experiment of millimeter-scale droplet spreading on the rigid substrate and the numerical simulation under the same conditions were carried out. The consistency between the experimental and simulation results has revealed that the VOF model is considerably effective. After that, the effects of the particle size and wettability of powder on the spreading behavior of micro binder droplets were studied through the numerical simulation method based on the VOF model. With the analysis and summary of the microdroplets' spreading behaviors, the results have shown that the particle size and wettability of the powder greatly influence the spreading behaviors of the droplet. Finally, the characterization of the actual printed samples showed that the optimal process parameters obtained by the simulation study are close to the results of the experimental 3D printing process. In conclusion, the numerical simulation method proposed in this paper can effectively analyze the influence of particle-droplet interaction on the 3D printing process. The results also demonstrated that the droplet impact behavior was governed by the physical and dynamic characteristics of the binder/powder interaction system, rather than the only properties of binder droplet. An enhanced understanding of this interaction with this method might enable substantially higher printing accuracy and the biological activity while optimizing the amount of acid binder in the 3D printing process. Besides, it is a more efficient way to explore new materials' printability applied to 3D printing of bone tissue engineering scaffolds.