Physics-based nozzle design rules for high-frequency liquid metal jetting

We present physics-based nozzle design rules to achieve high-throughput and stable jetting in drop-on-demand liquid metal 3D printing. The design rules are based on scaling laws that capture the change in the meniscus oscillation relaxation time with geometric characteristics of the nozzle's inner profile. These characteristics include volume, cross-sectional area, and inner surface area of the nozzle. Using boundary layer theory for a simple geometry, we show that the meniscus settles faster when the ratio of inner surface area to volume is increased. High-fidelity multiphase flow simulations verify this scaling. We use these laws to explore several design concepts with parameterized classes of shapes that reduce the meniscus relaxation time while preserving desired droplet specifications. Our findings enable exploration of nozzle concepts that can achieve optimal performance by increasing the ratio of the circumferential surface area to the bulk volume to the extent that is allowable by manufacturing constraints.