Spreading Dynamics of an Impinging Ferrofluid Droplet on Hydrophilic Surfaces under Uniform Magnetic Fields

This paper reports a numerical investigation on the spreading dynamics of an impinging ferrofluid droplet on solid hydrophilic surfaces (i.e., theta(w) <= 60 degrees) in the presence of uniform magnetic fields. A finite element method-based commercial solver is implemented to perform several numerical simulations, which uses a phase-field (PF) method to couple both the flow and magnetic fields. The results demonstrate that a uniform magnetic field is capable of controlling the spreading dynamics of an impinging droplet on hydrophilic substrates. Additionally, the application of a magnetic field results in the generation of a steady-state droplet shape with a reduced base diameter and an increased apex height at higher magnetic Bond numbers at the end of the spreading process. Moreover, as the viscosity of the droplet decreases, the droplet experiences an increase in its primary spreading diameter, which can be even reduced through the implementation of a vertical uniform magnetic field. Additionally, an oscillatory motion appears in a droplet during the spreading phenomenon at lower Ohnesorge numbers (i.e., Oh = 0.023), which is further sustained for a longer period of time in the relaxation phase with increased amplitudes in the case of an extremely low-viscosity droplet (i.e., Oh = 0.002) before attaining a final equilibrium shape. Furthermore, at Oh = 0.002, the droplet undergoes a breakup event after the impact for a short period of time, while the magnetic field induces an elastic behavior in a droplet at lower viscosities (i.e., Oh = 0.023) during the free fall under gravity.