Numerical investigation on frequency shift of an electromagnetically levitated molten droplet

The oscillating droplet method using electromagnetic levitation is a superior way for measuring the surface tension of molten materials, especially for reactive and refractory melts. Through frequency analysis of droplet motions, oscillation frequency is obtained and Rayleigh's theory is applied to determine the surface tension. However, the Rayleigh's theory presumes that the droplet is spherical with small deformation in Legendre's expressions and oscillates freely. Such prerequisites are hard to realize in reality and frequency shifts are introduced inevitably. In this work, a series of axisymmetric simulations are performed to investigate the frequency shift due to irregular deformation and positioning force exerted on an electromagnetically levitated droplet. The arbitrary Lagrange-Euler method is adopted for tracing the free surface of the droplet. The results found that the droplet deformation increases with increasing heating current and droplet radius, which leads to a negative frequency shift. On the contrary, the positioning current induces a positive frequency shift. The frequency shift caused by irregular deformation can be balanced by that induced by positioning current and a rather accurate oscillation frequency can be achieved when an appropriate positioning current is imposed, which is determined to be 121.5-146.0 A for deformation rate of ξ = 1.101 to ξ = 1.875 for silver droplet. With this work, it is expected to provide guidelines for better arranging operating parameters of EML device and improving the measurement accuracy of surface tension when the frequency shift caused by irregular deformation and external electromagnetic force are taken into account.