Formation mechanisms and morphological transitions of compound droplets in ferrofluid systems

This study develops an axisymmetric multiphase flow model for non-conducting ferrofluids in cylindrical coordinates, based on Maxwell's equations and the phase field method. The governing equations are solved using a high-accuracy spectral element method. The model is validated through a series of benchmark simulations, including Laplace's law for stationary droplets, the deformation of non-magnetic droplets under uniform magnetic fields, and the coalescence of bubble pairs. Subsequent simulations investigate the effects of surface tension ratio, magnetic field strength, droplet size, and density ratio on the formation of compound droplets composed of magnetic and non-magnetic droplets in a non-magnetic fluid. Results indicate that the surface tension ratio is the primary determinant of droplet morphology, yielding three distinct morphologies under varying ratios: dumbbell-shaped structures, magnetic droplet encapsulating non-magnetic droplet, and the inverse encapsulation. For a surface tension ratio of 1:1:1, the contact time between droplets first decreases and then increases with increasing magnetic field strength. When the surface tension ratio is set to 3:1:1, reducing either the radius of the non-magnetic droplet radius or the density ratio slows the ascent velocity of the non-magnetic droplet, thus shortening contact time. When the two droplets have identical densities, decreasing the radius of the non-magnetic droplet slightly enhances encapsulation. Furthermore, simultaneous reduction of both the density ratio and non-magnetic droplet radius drives the compound droplet morphology to transition from semi-encapsulation to full encapsulation. The formation of fully encapsulated compound droplets primarily depends on surface tension ratios, with synergistic contributions from droplet sizes and density ratios.