General equation describing viscosity of metallic melts under horizontal magnetic field

Viscosities of pure Ga, Ga₈₀Ni₂₀, and Ga₈₀Cr₂₀ metallic melts under a horizontal magnetic field were investigated by a torsional oscillation viscometer. A mathematical physical model was established to quantitatively describe the viscosity of single and binary metallic melts under a horizontal magnetic field. The relationship between the viscosity and the electrical resistivity under the horizontal magnetic field was studied, which can be described as η_B=η+(2H)/(πΩ)B² (η_B is the viscosity under the horizontal magnetic field, η is the viscosity without the magnetic field, H is the height of the sample, Ω is the electrical resistivity, and B is the intensity of magnetic field). The viscosity under the horizontal magnetic field is proportional to the square of the intensity of the magnetic field, which is in very good agreement with the experimental results. In addition, the proportionality coefficient of η_B and quadratic B, which is related to the electrical resistivity, conforms to the law established that increasing the temperature of the completely mixed melts is accompanied by an increase of the electrical resistivity. We can predict the viscosity of metallic melts under magnetic field by measuring the electrical resistivity based on our equation, and vice versa. This discovery is important for understanding condensed-matter physics under external magnetic field.