Collisional ferrohydrodynamics of magnetic fluid droplets on superhydrophobic surfaces

Abstract

The study reports the aspects of post-impact hydrodynamics of ferrofluid droplets on superhydrophobic (SH) surfaces in the presence of a horizontal magnetic field. A wide gamut of dynamics was observed by varying the impact Weber number (We), the magnetic field strength (manifested through the magnetic Bond number (Bom), which is defined as the ratio of magnetic force to surface tension force), and the Hartmann number (Ha), defined as the ratio of magnetic force to the viscous force. For a fixed We ∼ 60, we observed that at moderately low Bom ∼300, droplet rebound off the SH surface is suppressed. The noted We is chosen to observe various impact outcomes and to reveal the consequent ferrohydrodynamic mechanisms. We also show that ferrohydrodynamic interactions lead to asymmetric spreading due to variation in magnitude of the Lorentz force, and the droplet spreads preferentially in a direction orthogonal to the magnetic field lines. We show analytically that during the retraction regime, the kinetic energy of the droplet is distributed unequally in the transverse (orthogonal to the external horizontal magnetic field) and longitudinal (along the direction of the magnetic field) directions. This ultimately leads to the suppression of droplet rebound. We studied the role of Bom at fixed We ∼ 60 and observed that the liquid lamella becomes unstable at the onset of retraction phase, through nucleation of holes, their proliferation and rupture after reaching a critical thickness only on SH surfaces, but is absent on hydrophilic surfaces. We propose an analytical model to predict the onset of instability at a critical Bom. The model shows that the critical Bom is a function of the impact We, and the critical Bom decreases with increasing We. We illustrate a phase map encompassing all the post-impact ferrohydrodynamic phenomena on SH surfaces for a wide range of We and Bom.