Thermocapillary migration of a conductive droplet on a non-isothermal plate under a magnetic field

The thermocapillary migration of an electrically conductive droplet on a non-isothermal substrate under the influence of a magnetic field is investigated numerically. In the absence of a magnetic field, the transient migration process consists of three stages: acceleration, deceleration, and stable migration. The stable migration velocity exhibits non-monotonic variation with respect to the substrate wettability. When a magnetic field is applied, the Lorentz force suppresses both the maximum and stable migration velocities, causing the deceleration stage to vanish at high Hartmann numbers. The critical contact angle for the migration direction reversal approaches 90° as Hartmann number increases, due to the suppression of Marangoni flows by the magnetic field. Additionally, the Lorentz force aligns streamlines with the magnetic field by inhibiting horizontal fluid motion. Using lubrication theory, the stable migration velocity of droplets with small contact angles is derived, and the resulting scaling laws show excellent agreement with numerical simulations.