Dynamic study of ferrodroplet and bubbles merging in ferrofluid by a simplified multiphase lattice Boltzmann method

In this article, the dynamics of ferrodroplet deformation and bubbles merging within the ferrofluid under a uniform magnetic field are studied through numerical simulations. A recently developed simplified multiphase lattice Boltzmann method (SMLBM) is used to capture the hydrodynamic behavior of ferrofluids, the Cahn-Hilliard (CH) equation is employed as the interface tracking algorithm, whose solution is also obtained within the lattice Boltzmann framework and a self-correcting procedure is used to solve the magnetic field along with conjugate boundary conditions for a smooth transition of magnetic permeability at the interface. A series of numerical simulations are performed for a range of magnetic field strength, magnetic susceptibility and Ohnesorge number (Oh), along with a comparison between obtained results and previous experimental and numerical results. The dynamical behavior of ferrodroplets and bubbles merging in ferrofluids is analyzed through the distribution of magnetic field and magnetic flux density, velocity contours, pressure variations, the magnetic energy density and the effect of inertia. Findings of this study may help to explain the mechanism of ferrodroplet deformation and merging of bubbles within the ferrofluid and provide a useful insight into the distribution of flow variables during these deformations and merging phenomena.