Numerical simulation of two-phase flows in the presence of a magnetic field

A set of non-dimensional model equations, which can simulate incompressible, immiscible two-phase flows in the presence of a magnetic field, has been derived and solved numerically with a finite difference method using the HSMAC algorithm. In this study, dynamics of a falling droplet of liquid metal into a horizontal liquid metal layer and of a rising air bubble in water subject to a magnetic field are presented as examples. The numerical results reveal that the Lorentz force acts to dampen the motion of electric conducting fluid as the Hartmann number increases. On the other hand, even for ordinary non-conducting fluids such as water and air, a substantial body force due to magnetization influences the air bubble behaviour in water under a gradient magnetic field.