Computational design of optimal nozzle shape for liquid metal jetting using scaling analysis and multiphase flow simulation*

We present physics-driven nozzle design rules to achieve fast and stable jetting in drop-on-demand liquid metal 3D printing. The design rules are based on scaling laws that capture the change of meniscus oscillation relaxation time with geometric parameters of the nozzle's inner profile. The nozzle geometry is parameterized by bulk volume, cross-sectional area, and circumferential area of the inner channel. We employed the Navier-Stokes equation and the Stokes boundary layer theory to derive a hypothesis for scaling rule of viscous dissipation at the meniscus of the nozzle outlet. The scaling of relaxation time of the meniscus is inversely proportional to the circumferential surface area to the volume of the nozzle. The proposed scaling rule is demonstrated by multiphase flow simulations. Using OpenFOAM multiphase flow solver, we performed several simulations of oscillatory dynamics of multiphase interface between liquid metal (Al) and Argon gas under a pressure gradient across the nozzle and the surface tension. Informed by our analytical and numerical investigations, we present several design concepts with parameterized classes of shapes for optimal performance of 3D printing nozzle.