Strong Deformation of Ferrofluid-Filled Elastic Alginate Capsules in Inhomogenous Magnetic Fields

We present a new system based on alginate gels for the encapsulation of a ferrofluid drop, which allows us to create millimeter-sized elastic capsules that are highly deformable by inhomogeneous magnetic fields. We use a combination of experimental and theoretical work in order to characterize and quantify the deformation behavior of these ferrofluid-filled capsules. We introduce a novel method for the direct encapsulation of unpolar liquids by sodium alginate. By adding 1-hexanol to the unpolar liquid, we can dissolve sufficient amounts of CaCl₂ in the resulting mixture for ionotropic gelation of sodium alginate. The addition of polar alcohol molecules allows us to encapsulate a ferrofluid as a single phase rather than an emulsion without impairing ferrofluid stability. This encapsulation method increases the amount of encapsulated magnetic nanoparticles resulting in high deformations of approximately 30% (in height-to-width ratio) in inhomogeneous magnetic field with magnetic field variations of 50 mT over the size of the capsule. This offers possible applications of capsules as actuators, switches, or valves in confined spaces like microfluidic devices. We determine both elastic moduli of the capsule shell, Young's modulus and Poisson's ratio, by employing two independent mechanical methods, spinning capsule measurements and capsule compression between parallel plates. We then show that the observed magnetic deformation can be fully understood from magnetic forces exerted by the ferrofluid on the capsule shell if the magnetic field distribution and magnetization properties of the ferrofluid are known. We perform a detailed analysis of the magnetic deformation by employing a theoretical model based on nonlinear elasticity theory. Using an iterative solution scheme that couples a finite element/boundary element method for the magnetic field calculation to the solution of the elastic shape equations, we achieve quantitative agreement between theory and experiment for deformed capsule shapes using the Young modulus from mechanical characterization and the surface Poisson ratio as a fit parameter. This detailed analysis confirms the results from mechanical characterization that the surface Poisson ratio of the alginate shell is close to unity, that is, deformations of the alginate shell are almost area conserving.