Numerical and theoretical analysis for deformation of a ferrofluid droplet in shear flow under magnetic field*

We numerically investigated a deformation of a ferrofluid droplet in shear flow under the uniform magnetic field. We employed the boundary integral method to calculate the incompressible two-phase Stokes flow and the magnetic field governed by Maxwell’s equation. In the validation problems, we checked that the simulation results were in good agreements with previous numerical and theoretical studies. Our simulation results suggested that imposing magnetic fields perpendicular to the shear flow suppresses the droplet deformation and breakup.

Furthermore, we derived an equation to predict the droplet deformation affected by the magnetic field. The prediction equation was based on the velocity boundary condition and the stress balance on the droplet surface and given by the eigenvalues of a composite stress tensor originated by the shear flow and magnetic field. The numerical and theoretical results showed good agreement under small deformation in the wide range of the viscosity ratio between the external fluid and the ferrofluid droplet.

These results may contribute to enhancing the potential of the ferrofluid droplet and accelerating the development of applications using it.