We elucidate the phenomena of dynamic wetting, shape evolution and splitting of ferrofluid (FF) droplets on a hydrophobic surface under the influence of a magnetic field. In the case of a FF droplet interacting with a magnetic field, both surface energy and magnetic energy contribute to the total Gibb's free energy and hence the wetting phenomena. The nanoparticles in the FF droplet migrate and get accumulated at the apex of the droplet which enhances the magnetic interaction causing large deformation of the droplet. The FF droplet deformation and subsequent splitting are governed by the interplay between the magnetic Fm and surface tension Fs forces. The ratio of the forces km = (Fm/Fs) was found to be a function of the magnetic Bond number Bom and non-dimensional gap g* as km ∼ (Bom)0.3(g*)-0.86. Splitting of the FF droplets was observed for km > 1 and for km < 1, an equilibrium droplet shape was observed. The wetting behavior of the FF droplets was found to be strongly dependent on the FF concentration c - concentrated (c = 1.2%) FF droplets exhibit contact line (CL) pinning and decrease in contact angle (CA) θ with time throughout, while diluted (c = 0.6%) FF droplets show a mixed mode (CL pinning followed by constant CA). In splitting of FF droplets, the ratio of the volume of the daughter droplet to that of the parent droplet i.e. (Vd/Vp), was found to decrease with an increase in the parent droplet size Vp.
We report the dynamics of aqueous droplets of different size and viscosity at the interface of a coflowing stream of immiscible oils (i.e., primary and secondary continuous phases) in a microchannel, at low Re. The lateral migration of droplets introduced into the primary continuous phase toward the interface and subsequent selective migration of droplets across the interface into the secondary continuous phase is investigated. The interplay between the competing noninertial lift and interfacial tension forces, which govern the interfacial migration of the droplets, is presented and discussed. The velocity and strain rate profiles, and interface location, which are critical for calculating the lift force and migration behavior of droplets, are presented. The trajectories of droplets of different size and viscosity in the primary continuous phase are obtained for different interface locations. During interfacial migration, the deformation behavior of droplets of different viscosities is studied. Finally, sorting of droplets based on size contrast is demonstrated and sorting efficiency is found. A new paradigm of migration and sorting of droplets is reported, which could find importance in chemical and biological applications.
Droplets can be used as carrier vehicles for the transportation of biological and chemical reagents. Manipulation of water-and oil-based ferromagnetic droplets in the presence of a magnetic field has been well-studied. Here, we elucidate the transport of a sessile aqueous (diamagnetic) droplet placed over spikes of oil-based ferrofluid (FF) in the presence of a nonuniform magnetic field. An oil-based FF droplet, dispensed over a rigid oleophilic surface, interacts with a magnetic field to get transformed into an array of spikes which then act as a carrier for the transportation of the aqueous droplet. Our study reveals that transportation phenomena is governed by the interplay of three different forces: magnetic force F m , frictional force F f , and interfacial tension force F i , which is expressed in terms of the magnetic Laplace number (La m ) and magnetic Bond number (Bo m ) as La m −1 = (F f1 /F m,x ) and Bo m La m −1 = (F f2 /F i ). Based on the values of the dimensionless numbers, three different regimes, steady droplet transport, spike extraction, and magnet disengagement, are identified. It is found that steady droplet transport is observed for La m −1 ≤ 1 and Bo m La m −1 ≤ 1, whereas extraction of spikes is observed for La m −1 ≤ 1 and Bo m La m −1 > 1 and magnet disengagement is observed for La m −1 > 1.In the steady droplet transport regime, velocity of the aqueous droplet U ds was found to be dependent on the volumes of the aqueous droplet V w and FF droplet V FF following U ds ∼ V w −0.19 V FF 0.36 . A simple model is presented that accurately predicts the aqueous droplet velocity U ds within 5% of the corresponding experimental data. In the spike extraction regime, the spike extraction distance L se was found to vary with V w , V FF , and the magnet velocity U ms following L se ∼ V w −1.75 V FF 0.75 U ms −1.56 .
Manipulation of aqueous droplets in microchannels has great significance in various emerging applications such as biological and chemical assays. Magnetic-field based droplet manipulation that offers unique advantages is consequently gaining attention. However, the physics of magnetic field-driven cross-stream migration and the coalescence of aqueous droplets with an aqueous stream are not well understood. Here, we unravel the mechanism of cross-stream migration and the coalescence of aqueous droplets flowing in an oil based ferrofluid with a coflowing aqueous stream in the presence of a magnetic field. Our study reveals that the migration phenomenon is governed by the advection (τa) and magnetophoretic (τm) time scales. Experimental data show that the dimensionless equilibrium cross-stream migration distance δ* and the length Lδ* required to attain equilibrium cross-stream migration depend on the Strouhal number, St = (τa/τm), as δ* = 1.1 St0.33 and Lδ*=5.3 St−0.50, respectively. We find that the droplet-stream coalescence phenomenon is underpinned by the ratio of the sum of magnetophoretic (τm) and film-drainage time scales (τfd) and the advection time scale (τa), expressed in terms of the Strouhal number (St) and the film-drainage Reynolds number (Refd) as ξ = (τm + τfd)/τa = (St−1 + Refd). Irrespective of the flow rates of the coflowing streams, droplet size, and magnetic field, our study shows that droplet-stream coalescence is achieved for ξ ≤ 50 and ferrofluid stream width ratio w* < 0.7. We utilize the phenomenon and demonstrated the extraction of microparticles and HeLa cells from aqueous droplets to an aqueous stream.
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