## 2 Material and Methods
### The Validity of the VOF Model  
In order to test the VOF model proposed in this study, the observation experiments of millimeter-scale droplets spreading on the rigid substrate and the numerical simulations were carried out under the same conditions. What needs to be noted is that the millimeter-scale droplet is much easier to be generated and captured with common experimental equipment. The schematic diagram of test equipment is shown in Figure 3a-d.  
The spreading behaviors were recorded using a high-speed camera (SA-X2, Photron, Tokyo, Japan) with 10,000 frames per second (_fps_) capability, and the images were saved in 1024 \(\times\) 1024 pixels for subsequent analysis (shown in Figure 3b). A syringe (1 cm\({}^{3}\)) with a nozzle (32 G \(\times\) 4 mm) was used to simulate the pure water droplet sprayed from the printhead. The water droplets detach off the nozzle with an initial speed of zero by slowly squeezing the syringe (shown in Figure 3a). The droplets' impact velocities were adjusted by regulating the height of the droplets falling off the nozzle. The diameters of the water droplets were about 2.2 mm, and the impact velocities were about 1 m/s in this experiment. The actual impact velocity of the droplet was then corrected according to the results of the photos taken by the high-speed camera. The multi-particle/sphere substrate was prepared by high precision stereolithography equipment (lite600, Union Tech, Shanghai, China). The single-particle size of the substrate was 1 \(\pm\) 0.05 mm in diameter. The CAD design model is shown in Figure 3c, and the solid model is shown in Figure 3d. The simulations were carried out under the condition similar to the actual experimental parameters, in which the droplet diameter was 2.2 mm, the velocity is 0.991 m/s, density was 0.998 \(\times\) 10\({}^{3}\) kg/m\({}^{3}\), the viscosity was 0.894 mPa-s, the surface tension was 71.94 mN/m, and the particle diameter of the substrate was 1.0 mm, and the Weber number was 30.52.The static contact angle of the substrate material with pure water was 92\({}^{\circ}\), which was measured to be used as an attached boundary condition for the numerical simulations.  
In the results analysis, the spreading ratio \(\varepsilon\) was defined as the ratio of the spreading diameter of the droplet to its initial diameter, which is a key parameter to evaluate the binder droplet spreading behavior on the bioceramic particle surface. The spreading ratio \(\varepsilon\) is defined as follows:  
\[\varepsilon=\frac{D_{l}}{D_{0}}\]  
where \(D_{l}\) is the spreading diameter of the droplet, and \(D_{0}\) is the initial diameter of the binder droplet.  
During the whole collision process, the shape of the water droplet changing at different times can be accurately reproduced by consistent simulation (see the image in Figure 3f). While comparing the experimental data with simulation results (Figure 3e), the error of maximum spreading ratio was less than 3.1%. Considering that the simulation resultsare based on ideal conditions, the results were acceptable. The agreements between the simulation results and the experimental data suggest that the VOF model effectively simulated the droplet impacting process.