The breakup phenomenon of a ferrofluid droplet in a simple shear flow under a uniform magnetic field is numerically investigated in this paper. The numerical simulation, based on the finite element method, uses a level set method to capture the dynamic evolution of the droplet interface between the two phases. Focusing on small Reynolds numbers (i.e., Re ≤ 0.03), systematic numerical simulations are carried out to analyze the effects of magnetic field strength, direction, and viscosity ratio on the breakup phenomenon of the ferrofluid droplet. The results suggest that applying a magnetic field along α = 45° and 90° relative to the flow direction initiates breakup in a ferrofluid droplet at a low capillary number in the Stokes flow regime, where the droplet usually does not break up in a shear flow alone. At α = 0° and 135°, the magnetic field suppresses breakup. Also, there exists a critical magnetic bond number, Bocr, below which the droplet does not rupture, which is also dependent on the direction of the magnetic field. Additionally, the effect of the viscosity ratio on droplet breakup is examined at variable magnetic bond numbers. The results indicate a decrease in the critical magnetic bond number Bocr values for more viscous droplets. Furthermore, more satellite droplets are observed at α = 45° compared to α = 90°, not only at higher magnetic field strengths but also at larger viscosity ratios.


Mechanical and Aerospace Engineering

Research Center/Lab(s)

Center for Research in Energy and Environment (CREE)


The authors gratefully acknowledge the financial support from the Department of Mechanical and Aerospace Engineering (MAE) and the Center for Biomedical Research (CBR) at Missouri University of Science and Technology.

Keywords and Phrases

Magnetic field effects; Numerical methods; Numerical models; Polymer blends; Reynolds number; Shear flow; Viscosity, Dynamic evolution; Low capillary numbers; Low Reynolds number; Magnetic field strengths; Satellite droplets; Simple shear flow; Stokes flow regime; Uniform magnetic fields, Drop breakup

International Standard Serial Number (ISSN)

1070-6631; 1089-7666

Document Type

Article - Journal

Document Version

Final Version

File Type





© 2019 The Authors, All rights reserved.

Publication Date

01 Dec 2019