A numerical investigation on the deformation of ferrofluid droplets

In this paper, the dynamical mechanism and a general deformation law of a ferrofluid droplet suspended between the air and a liquid substrate under the action of the applied vertical uniform magnetic field are investigated by a numerical model. A generalized conservative phase-field simplified multiphase lattice Boltzmann model is adopted to solve the flow field and phase field, which has a good ability to simulate the problems of ternary fluid flows with large density ratios. Subsequently, the Maxwell equation of static magnetic field is used to solve the magnetic field using a self-correcting scheme. We used this model to numerically study the dynamic evolvement process of ferrofluid droplets placed between the air and a liquid substrate, which are exposed in a vertical uniform magnetic field. Some typical characteristics are employed to characterize the droplet shape, and it is found that the aspect ratio, the elongated velocity, and the height of the mass center of the ferrofluid droplet are related to the magnetic Bond number. Furthermore, the numerical results obtained with the model are in good agreement with the experimental results available in the literature. Finally, the quantitative power law relation between the magnetic Bond number and the aspect ratio of ferrofluid droplets is obtained by using the method of scaling law, which provides a theoretical basis for the study of the deformation mechanism and the universal laws of a ferrofluid droplet placed between the air and a liquid substrate under the action of the vertical uniform magnetic fields with different intensities.