Transport of a Sessile Aqueous Droplet over Spikes of Oil Based Ferrofluid in the Presence of a Magnetic Field.

Abstract

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 Fm, frictional force Ff, and interfacial tension force Fi, which is expressed in terms of the magnetic Laplace number ( Lam) and magnetic Bond number ( Bom) as Lam?1 = ( Ff1/ Fm, x) and Bom Lam?1 = ( Ff2/ Fi). 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 Lam?1 ? 1 and Bom Lam?1 ? 1, whereas extraction of spikes is observed for Lam?1 ? 1 and Bom Lam?1 > 1 and magnet disengagement is observed for Lam?1 > 1. In the steady droplet transport regime, velocity of the aqueous droplet Uds was found to be dependent on the volumes of the aqueous droplet Vw and FF droplet VFF following Uds ? Vw?0.19 VFF0.36. A simple model is presented that accurately predicts the aqueous droplet velocity Uds within 5% of the corresponding experimental data. In the spike extraction regime, the spike extraction distance Lse was found to vary with Vw, VFF, and the magnet velocity Ums following Lse ? Vw?1.75 VFF0.75 Ums?1.56.