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Ferrofluids are typically suspensions of magnetite nanoparticles, and behaveas a homogeneous continuum. The production of nanoparticles with a narrow sizedistribution and the achievement of colloidal stability are importanttechnological issues. The ability of the ferrofluid to respond to an externalmagnetic field in a controllable manner has made it emerge as a smart materialin a variety of applications, such as seals, lubricants, electronics cooling,shock absorbers and adaptive optics. Magnetic nanoparticle suspensions havealso gained attraction recently in a range of biomedical applications, such ascell separation, hyperthermia, MRI, drug targeting and cancer diagnosis. Inthis review, we provide an introduction to mathematical modeling of threeproblems: motion of superparamagnetic nanoparticles in magnetic drug targeting,the motion of a ferrofluid drop consisting of chemically bound nanoparticleswithout a carrier fluid, and the breakage of a thin film of a ferrofluid.

Ferrofluids and magnetically guided superparamagnetic particles in flows: A review of simulations and modeling