Maximum spreading of a ferrofluid droplet under the effect of magnetic field

This study presents a theoretical and an experimental study of the effects of an applied external magnetic field on the maximum spreading of a ferrofluid droplet impacting on a solid substrate. Although many studies have explored the theoretical modeling of the droplet impact scenario, a theoretical model representing the impact of ferrofluid droplets of different magnetic characteristics, strongly affected by the magnetic field, is yet to be addressed. In this study, we developed a theoretical model based on the principle of the conservation of energy to predict the maximal deformation of both diamagnetic and paramagnetic ferrofluid droplets upon impact under the influence of the magnetic field. The physics behind the variation of maximum drop spread, as a function of Weber number (We), Reynolds number (Re), and magnetic Bond number (Bom) for 5–45, 150–400, and 150–3000, respectively, was studied. By validating the theoretical model with the experimental observations, we demonstrated that the proposed theoretical model could successfully predict experimental observations. Through theoretical analysis and extensive experimental investigations, a rational understanding was formulated which allowed us to comment on the effect of all the governing dimensionless numbers (We, Re, and Bom) on the maximum spreading of a ferrofluid droplet upon impact.