Sedimentation dynamics of ferrofluid droplets under magnetic field

Resumo

Understanding the controlled manipulation of droplet dynamics in multiphase systems is crucial for improving oil-water separation processes in the petroleum industry. The application of external magnetic fields to ferrofluid droplets offers a promising strategy for enhancing phase segregation in magnetic emulsions. This study presents a numerical investigation of the sedimentation behavior of a single ferrofluid droplet due to gravity, subjected to uniform magnetic fields applied in horizontal or vertical orientations. A magnetohydrodynamic (MHD) model was developed and implemented in the Basilisk open-source framework, using direct numerical simulation (DNS). The software resolves variable density and viscosity fields with second‑order accuracy in time and space and employs the Bell–Colella–Glaz second‑order upwind scheme for velocity advection. Interface dynamics were captured with the Volume of Fluid (VoF) method, incorporating balanced continuous surface force formulation for surface tension and magnetic forces through the Kelvin force. The simulations reveal that magnetic field orientation critically affects droplet deformation and terminal velocity. The magnetic effects intensify with reduced surface tension. These results provide insights into magnetic control strategies for optimizing droplet separation processes in petroleum engineering applications involving ferrofluid emulsions.