In this project we seek to use mathematical theory to demonstrate a proof-of-concept ability to create shape-shifting smart liquids with a controllable surface morphology. The approach taken will be to analyse possible geometries theoretically using a combination of analytic and numerical techniques, including boundary integral methods. Specifically, we propose to analyse how a magnetic field can be used to force a ferrofluid with a free surface (a liquid-air interface) into certain desired shapes. Ferrofluids consist of magnetisable particles of sizes 10 nm or less suspended in a carrier fluid and coated with surfactants in order to prevent clumping. They behave as Newtonian fluids but with special superparamagnetic properties: when a magnetic field is switched on, particles undergoing Brownian motion align with the field lines inducing a significant non-local response on the fluid and return (almost instantaneously) to their Brownian motion state when the field is switched off. The ability to control ferrofluid surfaces using particular field configurations has been demonstrated for creating surface spikes (e.g. Lloyd et al. 2015), for controlling liquid-liquid interfaces Yecko 2010), and for propagating solitary waves (Blyth & Parau 2014). It is well known that while a cylindrical column of ordinary liquid (such as water) will naturally disintegrate into droplets as a consequence of a surface tension-driven instability, a ferrofluid column can be stabilised to maintain the columnar shape by use of an azimuthal magnetic field. Stabilising other geometrical equilibrium configurations will be investigated including, for example, a toroidal `doughnut’ shape, and a liquid helix. The ability to stabilise a liquid mass into these and other geometrical shapes can be viewed as a first step toward the design of liquid robots with total fluid-surface controllability.
This PhD project will be jointly supervised (50:50) by Dr Mark Blyth and Dr Robert Whittaker in the School of Mathematics.
