Solidification of a water-based sessile magnetic drop under the effect of a vertical magnetic field

The study, presented here, investigates the solidification time and height of water-based magnetic fluid, which is responsive to the magnetic field. Liquid solidification via freezing is ubiquitous in nature and affects several aspects of our daily lives and many industrial applications. However, little is known about a comprehensive model that can predict the freezing or solidification rate of a colloidal droplet while the freezing occurs under the influence of external body forces. In this study, we develop a mathematical model to describe a magnetic drop freezing on a solid substrate under the effect of a vertically oriented magnetic field. This model accounts for the strength of the actuating field, and the physical properties of liquid and ice (solid), in addition to the associated interfacial and surface energies and curvature of the droplet. The mathematical model formulated here is based on the mass, momentum, and energy conservation equation, which is eventually deduced to an equation similar to the lubrication equation accounting for the phase change and solidification height as a function of magnetic field strength. The solution of the governing equation will offer us a mechanism to control the solidification rate of the colloidal droplet, infused with metal nanoparticles, by tuning the magnetic field strength, which we also observed experimentally. In this study, We also proposed a magnetically influenced freezing time scale. Apart from academic interest, this study is essential to freeze casting and additive manufacturing of metallic and organic objects consisting of magnetic nanoparticles. In such processes, the solidification rate of a colloidal droplet dictates the pore morphology as well as the strength of the green body.