Wetting dynamics of a sessile ferrofluid droplet on solid substrates with different wettabilities

Abstract

There are several numerical approaches to define a permanent magnet in terms of mathematical equations, and each approach has progressed since its inception, but still endures some limitations on specific numerical phenomena. This study seeks to propose a novel numerical representation of a permanent magnet without incorporating its effect through boundary conditions, which overcomes the limitations of previous studies and enables us to introduce a magnetic field of desired strength at any location. A self-correcting method is modified to incorporate the magnetic field effects, while a simplified lattice Boltzmann method is utilized to solve the governing equations for flow field and interface. The validity of the proposed method is ensured by simulating some benchmark phenomena with and without the external magnetic field. This study also investigates the wetting dynamics of a sessile ferrofluid droplet deposited on solid substrates with different wettabilities. The influence of uniform and non-uniform magnetic fields on droplet spreading is discussed in detail. It is observed that for a non-uniform magnetic field in vertical direction, the ferrofluid droplet on a hydrophilic surface does not observe the spherical cap approximation unless the magnetic field strength is below saturation magnetization. Moreover, if the magnet is located above, the droplet undergoes large deformations and achieves pointy shapes with sharp tips on less wettable surfaces.