We numerically investigate the deformation and orientation of a ferrofluid droplet in a simple shear flow under a uniform magnetic field. The numerical simulation is based on the finite element method and couples the magnetic and flow fields. A level set method is used to model the dynamic motion of the droplet interface. Systematic numerical simulations are used to assess the effects of the direction and the strength of the magnetic field. Focusing on low Reynolds number flows (Re ≲ 0.02), the numerical results indicate that at a small capillary number (Ca ≈ 0.02), the magnetic field dominates over the shear flow above a certain magnetic bond number (Bom ≈ 3). The orientation of the droplet is aligned with the direction of the magnetic field, while the deformation of the droplet varies slightly when the direction of the magnetic field is varied. On the other hand, for large capillary numbers (Ca ≈ 0.23), the deformation and orientation of the droplet is influenced by both the shear flow and the magnetic field, except for a small magnetic bond number (Bom ≲ 0.2). In both the small and large capillary number cases, the droplet deformation is found to be maximum at α = 45° (the direction of magnetic field) and minimum at α = 135°. In addition, the effect of the magnetic field on the flow field inside and outside the droplet at different conditions is examined. We demonstrate active control of lateral migration of ferrofluid droplets in wall-bounded simple shear flows. The direction of the lateral migration depends on the orientation of the deformed droplets due to uniform magnetic fields at different directions.
The breakup phenomenon of a ferrofluid droplet in a simple shear flow under a uniform magnetic field is numerically investigated in this paper. The numerical simulation, based on the finite element method, uses a level set method to capture the dynamic evolution of the droplet interface between the two phases. Focusing on small Reynolds numbers (i.e., Re ≤ 0.03), systematic numerical simulations are carried out to analyze the effects of magnetic field strength, direction, and viscosity ratio on the breakup phenomenon of the ferrofluid droplet. The results suggest that applying a magnetic field along α = 45° and 90° relative to the flow direction initiates breakup in a ferrofluid droplet at a low capillary number in the Stokes flow regime, where the droplet usually does not break up in a shear flow alone. At α = 0° and 135°, the magnetic field suppresses breakup. Also, there exists a critical magnetic bond number, Bocr, below which the droplet does not rupture, which is also dependent on the direction of the magnetic field. Additionally, the effect of the viscosity ratio on droplet breakup is examined at variable magnetic bond numbers. The results indicate a decrease in the critical magnetic bond number Bocr values for more viscous droplets. Furthermore, more satellite droplets are observed at α = 45° compared to α = 90°, not only at higher magnetic field strengths but also at larger viscosity ratios.
Magnetic
digital microfluidics is advantageous over other existing
droplet manipulation methods, which exploits magnetic forces for actuation
and offers the flexibility of implementation in resource-limited point-of-care
applications. This article discusses the dynamic behavior of a pair
of sessile droplets on a hydrophobic surface under the presence of
a permanent magnetic field. A phase field method-based solver is employed
in a two-dimensional computational domain to numerically capture the
dynamic evolution of the droplet interfaces, which again simultaneously
solves the magnetic and flow fields. On a superhydrophobic surface
(i.e., θc = 150°), the nonuniform magnetic field
forces the pair of sessile droplets to move toward each other, which
eventually leads to a jumping off phenomenon of the merged droplet
from the solid surface after coalescence. Also, there exists a critical
magnetic Bond number Bo
m
cr, beyond which no coalescence event
between droplets is observed. Moreover, on a less hydrophobic surface
(θc ≤ 120°), the droplets still coalesce
under a magnetic field, although the merged droplet does not experience
any upward flight after coalescence. Also, the merging phenomenon
at lower contact angle values (i.e., θc = 90°)
appears significantly different than at higher contact angle values
(i.e., θc = 120°). Additionally, if the pair
of sessile droplets is dispersed to a different surrounding medium,
the viscosity ratio plays a significant role in the upward flight
of the merged droplet, where the coalesced droplet exhibits increased
vertical migration at higher viscosity ratios.
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