Shape evolution and splitting of ferrofluid droplets on a hydrophobic surface in the presence of a magnetic field

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 F-s forces. The ratio of the forces k(m) = (F-m/F-s) was found to be a function of the magnetic Bond number Bom and non-dimensional gap g* as k(m) similar to (B-om)(0.3)(g*)(-0.86). Splitting of the FF droplets was observed for k(m) > 1 and for k(m) < 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) theta 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. (V-d/V-p), was found to decrease with an increase in the parent droplet size V-p.