This
paper reports a numerical investigation on the spreading dynamics
of an impinging ferrofluid droplet on solid hydrophilic surfaces (i.e.,
θw ≤ 60°) 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.