Impact dynamics of ferrofluid droplet on a PDMS substrate under the influence of magnetic field

We report the impact dynamics of a ferrofluid droplet on a PDMS substrate in the presence of a non-uniform magnetic field. Based on high-speed imaging, we unravel the various characteristic behaviors of the impinging ferrofluid droplet under the influence of a vertically applied magnetic field. We show that the magnetic, viscous, inertial, and interfacial energies non-trivially affect the equilibrium shape of the impacting ferrofluid droplet. Consequently, we reveal that the collective role of these forces ensures the ferrofluid droplet exhibits essentially three typical equilibrium shapes, i.e., no spike, single spike, and multiple spikes assemblies. Based on a phase diagram, we demonstrate the role of various dynamic forces in dictating the droplet's equilibrium shape. We report the universality constant exhibited by the non-dimensionalized droplet diameter (ratio of the droplet's equilibrium diameter to the semi-minor axis width of the ellipsoidal droplet just before impact), irrespective of the magnetic Bond number, on a PDMS substrate to be around 1.3. Consequently, we investigated the internal flow domain of the ferrofluid flow field in the presence of a magnetic field, essentially to understand its characteristic spreading behavior. Following bright-field visualization, we observed chain-like clustering of the magnetic nanoparticles inside the ferrofluid flow domain in a direction perpendicular to the magnet. Insights from bright field visualization enable us to qualitatively argue that the chaining phenomena of the nano-sized particles (present inside ferrofluid) in a direction perpendicular to the substrate ensure the formation of single/multiple assemblies of spikes. In addition, we also argue that the chain-formation of the magnetic nanoparticles increases the viscous force of the ferrofluid droplet in the presence of a magnetic field. This augmented viscous energy of the fluid in the presence of a magnetic field ensures an inverse relationship of the spreading diameter with magnetic field strength. The inference of the present study could be beneficial in the rational design of wide-ranging applications, such as ink-jet printing or 3D printing, requiring controlled droplet spreading phenomena.