Three-dimensional simulation of micrometer-sized droplet impact and penetration into the powder bed

• We propose a numerical method to model micron-sized droplets impacting on the powder bed.
• The Cartesian grid based volume-of-fluid method is used to track the liquid-air interface.
• A contact angle model is proposed and implemented on the embedded solid objects.
• The impact velocity has strong effect on the droplet-powder interaction.
• Our method can be used to determine the optimal printing conditions in the inkjet-assisted 3D printing.

In recent years, various drop-on-demand inkjet technologies capable of precisely delivering micron-sized droplets have been adopted in a few novel powder-based 3D printing processes. The droplet-powder interaction is an important step in these 3D printing technologies. In this paper, we propose a direct numerical simulation method to study the micron-sized droplets impacting on the powder bed. Since the powder particle size in our study is comparable to that of impacting droplets, the powder bed is modeled with a large number of rigid solid spheres fixed in their positions during the droplet impact. A set of important dimensionless parameters and scaling arguments is presented to elucidate the underlying physics involved in the micron-sized droplets impacting on powder. The Cartesian grid based volume-of-fluid method is used to track the immiscible liquid and air interface during the droplet-powder interaction. A contact angle model is proposed to include the wetting effect of the liquid agent on powder particles. The proposed numerical methods are implemented in an open-source code Gerris. Two numerical tests relevant to our study are conducted to validate the modified simulation code. Finally, we carry out simulations of a micrometer-sized droplet impacting on the powder bed with three different impact velocities. For low impact velocity, the droplet can even gain the momentum in the early stage due to strong capillary forces at contact lines compared to inertial force. The large impact velocity results in a wider spread and deeper penetration, however the liquid distribution inside the powder bed can be segmented because of high impact energy. The numerical method proposed in our study can be used to design suitable droplet-powder systems as well as determine optimal printing conditions in the inkjet-assisted powder-based 3D printing technologies.