Hydrodynamic stability threshold of liquid metal current collectors

Abstract

A mechanism derived from hydrodynamic theory to explain the ejection instability of liquid metal current collectors is presented. The ejection mechanism is shown to be caused by the onset of the Kelvin–Helmholtz instability resulting from the gradient of azimuthal (primary) flow at the interface between the liquid metal and cover gas. This new mechanism differs from the previous theory developed by Eriksson [in Electrical Engineering Series, no. 48, edited by M. Luukkala (The Finnish Academy of Technical Sciences, Helsinki, Finland, 1982), who analyzed the onset of the Kelvin–Helmhotz instability resulting from the gradient of meridional (secondary) flow at the interface. Considering the solution to the linearized Navier–Stokes equations at the liquid metal and gas interface, the azimuthally driven (primary flow) instability mechanism for the onset of ejection is much more prevalent than the meridional (secondary) flow driven mechansim. Furthermore, Eriksson’s theory requires an empirical multiplicative fractional factor that is not physically justified to predict experimentally measured ejection points, whereas the present theory is more self-consistent. Calculations of minimum ejection values from both theories were compared with corresponding experimental ejection data. The present theory appears to give significantly better engineering estimates, both quantitively and qualitatively, for minimum ejection threshold than Eriksson’s theory. The basic mathemtical model presented can serve as the basis for developing a more complex mathematical model for liquid metal ejection.