Printability regimes of pure metals using contactless magnetohydrodynamic drop-on-demand actuation

We demonstrate a computational study used to evaluate drop-on-demand printability of liquid metals via a contactless magnetohydrodynamic (MHD) pumping method. We show that the ejection regimes of pure liquid metal droplets can be categorized using two dimensionless quantities: We and a new dimensionless quantity S = H a 2 C a. By plotting We vs S, a linear relationship emerges which relates the velocity through the ejection orifice to the applied magnetic flux density. Additionally, satellite-free droplet generation is shown to be bounded by the ranges 1000 ≲ S ≲ 2000 and 10 ≲We≲ 20. These ranges, coupled with the linear We vs S relationship, allow one to predict the critical magnetic flux necessary to eject a satellite-free liquid metal droplet for any liquid metal with a very low viscosity to surface tension ratio (O h < 0.005). We discuss the physics underlying the MHD ejection process and relate the pump action to the dimensionless quantities. We use an MHD finite element model to parametrically sweep through applied magnetic fields and explore two-phase ejection of Al, Cu, Fe, Li, Sn, Ti, Zn, and Zr droplets from a 200 μm orifice. The model is validated using experimental high speed video ejection of Zn and Al, and the reported relationship between We and S can be used to connect the input flux density to the resulting ejection regime.