Revisiting the Young’s model for ferrofluid droplets: Magnetowetting or magneto-dewetting?

Abstract

Magnetic field-mediated wetting of ferrofluid droplets has emerged to be of fundamental importance because of its plethora of applications ranging from chemical and biomolecular analysis to soft robotics and medical imaging. However, while extensive studies continue to be reported on the underlying experimental facets, a fundamental theoretical depiction of the observed contact angle variation with the applied magnetic field remains grossly elusive, as attributable to a complex dependence of the induced magnetization on the droplet’s intrinsic magnetic properties. Circumventing these constraints, here we put forward a first-principle analytical model that delineates the variation in the contact angle as a function of an applied magnetic field on a sessile ferrofluid droplet, by appealing to energy minimization principles. One key feature of our analysis is the consideration of the local magnetization as a function of the magnetic field itself, resulting in a new contribution to the interfacial energy by virtue of normal traction at the droplet's contact with its non-magnetic surroundings. This theory is supported by experiments identified in prior research to elucidate the fundamental physics of relevance. Our results highlight the substantial influence of the saturation magnetization and the initial susceptibility of the ferrofluid on the resulting contact angle alterations, as well as possible non-trivial routes of highly selective and precise enhancement or attenuation in the extent of wetting. These findings are likely to be of fundamental importance towards establishing the design foundations of portable magnetic resonance imaging devices, micromixers, and microreactors, magnetically-manipulated automatic control of soft fluidic matters, among others.