Effects of vertical magnetic field on impact dynamics of ferrofluid droplet onto a rigid substrate

Ferrofluid as a smart fluid has a wide range of applications. Although the spreading dynamics of water droplets have been well investigated, spreading dynamics of ferrofluid droplets under a magnetic field has rarely been studied. This paper reports our findings of the impact dynamics of a ferrofluid droplet onto a tempered glass surface in the presence of a vertical magnetic field. The effects of magnetic intensity, impact velocity, and $\mathrm{F}{\mathrm{e}}_3{\mathrm{O}}_4$ nanoparticle concentration were investigated. It turned out that with the increased magnetic intensity, the height of the ferrofluid droplet would decrease owing to the energy dissipation increase of ferrofluids under a magnetic field and the additional stretching force in the vertical direction. Interestingly, we found that exertion of the magnetic field could significantly diminish the influence of velocity differences on the droplet spread dynamics in height direction. Satellite droplets were also observed in certain cases when the rebound kinetic energy could overcome the restraint of surface tension and adhesion of viscosity in the presence of the magnetic field. Our work will be a significant reference to with regard to various practical applications, especially when the impact dynamics of ferrofluid droplets need to be under precise control, for instance, as in three-dimensional printing or spray coating, etc.

Figure 1

(a) Particle size distribution in ferrofluids of three different mass fractions, (b) comparison of density and viscosity between ferrofluids with different nanoparticle concentrations, (c) magnetization curve of $\mathrm{F}{\mathrm{e}}_3{\mathrm{O}}_4$ nanoparticles, and (d) hysteresis loop of $\mathrm{F}{\mathrm{e}}_3{\mathrm{O}}_4$ nanoparticles.

Figure 2

Magnetic intensity as a function of the current magnitude.

Figure 3

Schematic diagram of experimental system.

Figure 4

The shape changes of droplets after impacting a substrate surface. The length of the scale bars corresponds to 0.6 mm, and the nanoparticle concentration is 0.01 wt % in the absence of magnetic field.

Figure 5

Droplet spreading dynamics under vertical magnetic field at $U=0.86\mathrm{m}/\mathrm{s}$: (a) dimensionless diameter $D_d/D_0$, (b) dimensionless height $H_d/D_0$ as a function of time with 0.1% mass fraction $\mathrm{F}{\mathrm{e}}_3{\mathrm{O}}_4$ nanoparticles in varying magnetic fields.

Figure 6

(a) Dimensionless maximum spreading radius $D_{\max }/D_d$ at $t=0\mathrm{ms}$ and (b) maximum recoiling height $H_{\max }/D_d$ at $t=1.6\mathrm{ms}$ vs the magnetic field intensity for droplet without and with 0.1% nanoparticles, respectively.

Figure 7

Water and ferrofluid droplet spreading dynamics under vertical magnetic field at $U=0.86\mathrm{m}/\mathrm{s}$, $t=53.4\mathrm{ms}$: (a) dimensionless diameter and (b) dimensionless height as a function of magnetic field intensity.

Figure 8

Droplet spreading dynamics under vertical magnetic field: dimensionless height $H_d/D_0$ as a function of magnetic field with 0.1% mass fraction $\mathrm{F}{\mathrm{e}}_3{\mathrm{O}}_4$ nanoparticles and impact velocity $U=0.86$ and 1.82 m/s when $t=1.6\mathrm{ms}$.

Figure 9

Images showing particle movement in 0.1 wt % nanofluid droplets after applying the 1000-G magnetic field (a) in the absence of magnetic field, (b) 1 s after adding magnetic field, and (c) 2 s after adding magnetic field.

Figure 10

Image of satellite droplet when magnetic intensities are 400, 800, and 1000 G, impact velocity is 0.8 m/s, and $\mathrm{F}{\mathrm{e}}_3{\mathrm{O}}_4$ nanoparticle concentration is 0.01 wt %.