Nonmagnetic spheres confined in a ferrofluid layer (magnetic holes) present dipolar interactions when an external magnetic field is exerted. The interaction potential of a microsphere pair is derived analytically, with precise care for the boundary conditions along the glass plates confining the system. Considering external fields consisting of a constant normal component and a high frequency rotating in-plane component, this interaction potential is averaged over time to exhibit the average interparticular forces acting when the imposed frequency exceeds the inverse of the viscous relaxation time of the system. The existence of an equilibrium configuration without contact between the particles is demonstrated for a whole range of exciting fields, and the equilibrium separation distance depending on the structure of the external field is established. The stability of the system under out-of-plane buckling is also studied. The dynamics of such a particle pair is simulated and validated by experiments.

Many complex fluids are only available in tiny quantities or used in confined regions. The task of measuring their rheological properties is then a challenge. Here we present a method showing how the viscosity of very small volumes of ferrofluid may be measured using immersed nonmagnetic spherical microparticles. In the suspension these act as magnetic holes in the ferrofluid which may be manipulated by external magnetic fields. When the effects of nearby walls as well as other spheres are taken into account, the results are consistent with viscosity values reported from standard bulk measurement techniques.

No abstract

Nonmagnetic particles in magnetized ferrofluids have been denoted magnetic holes and are in many ways ideal model systems to test various forms of particle self assembly and dynamics. Some case studies to be reviewed here include:• Chaining of magnetic holes • Braid theory and Zipf relation used in dynamics of magnetic microparticles • Interactions of magnetic holes in ferrofluid layersThe objectives of these works have been to find simple characterizations of complex behavior of particles with dipolar interactions.