Theoretical foundation of electromagnetically-driven oscillating cup viscometer

The electromagnetically-driven oscillating cup viscometer (EOC viscometer) is a novel noncontact technique that has been used to simultaneously measure viscosity and electrical conductivity of liquid metals and molten semiconductors at high temperatures. Though there were already a few successful applications in the past, the theory of the EOC method has never been fully developed and examined in detail. This paper established an exact solution for the oscillatory flow that is coupled transient angular motion of the cylindrical cup in an EOC viscometer and provided options for different measurement methods based on EOC. The angular motion solution can be decomposed to three components, including the angular displacement at equilibrium state, fast decay, and damped oscillation, each of which is described by a series of motion parameters respectively. The dependences of these motion parameters on material properties of interest are quantitatively delineated with measurable experimental parameters for practical experimental conditions. Two practical methods are proposed, namely the rapid method, which mainly takes advantage of fast decay, and the quasi-steady state method, which uses only the information collected from the damped oscillation. The results of this study established a theoretical basis for EOC experimental design and clarified measurement methods based on different regimes of the working conditions of the EOC.