Journal of Engineering Mathematics

, Volume 107, Issue 1, pp 231–251 | Cite as

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

  • Shahriar Afkhami
  • Yuriko Renardy


Ferrofluids are typically suspensions of magnetite nanoparticles, and behave as a homogeneous continuum. 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.


Ferrofluid Superparamagnetic nanoparticles Thin film approximation Volume-of-Fluid method 



This work is partially supported by NSF-DMS-1311707 and NSF-CBET-1604351.


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Copyright information

© Springer Science+Business Media B.V. 2017

Authors and Affiliations

  1. 1.Department of Mathematical SciencesNew Jersey Institute of TechnologyNewarkUSA
  2. 2.Department of MathematicsVirginia Polytechnic Institute and State UniversityBlacksburgUSA

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