  Ferrofluids are typically suspensions of magnetite nanoparticles, and behave
as a homogeneous continuum. The production of nanoparticles with a narrow size
distribution and the achievement of colloidal stability are important
technological issues. The ability of the ferrofluid to respond to an external
magnetic field in a controllable manner has made it emerge as a smart material
in a variety of applications, such as seals, lubricants, electronics cooling,
shock absorbers and adaptive optics. Magnetic nanoparticle suspensions have
also gained attraction recently in a range of biomedical applications, such as
cell separation, hyperthermia, MRI, drug targeting and cancer diagnosis. In
this review, we provide an introduction to mathematical modeling of three
problems: motion of superparamagnetic nanoparticles in magnetic drug targeting,
the motion of a ferrofluid drop consisting of chemically bound nanoparticles
without a carrier fluid, and the breakage of a thin film of a ferrofluid.
