Magnetic field altered ferrofluid droplet deformation in the uniaxial extensional flow

Ferrofluid droplets find several applications in various biomedical and process engineering systems related to magnetohydrodynamic problems. This study deals with the ferrofluid droplet deformation dynamics under the joint influence of the uniform magnetic field and uniaxial extensional flow. Here, using the phase-field method, we have investigated an extensive range of governing parameters to analyze the droplet deformation in uniaxial extensional flows under uniform magnetic fields in the Stokes flow regime. Our model was validated against the seminal work of Stone and Leal (Stone, H. A. & Leal. L. G., 1989, J. Fluid Mech., 198, 399-427) for a system without an external magnetic field, and also with the experimental results of Afkhami et al. (Afkhami, S., Tyler, A. J., Renardy, Y., Renardy, M., ST. Pierre, T. G., Woodward, R. C., & Riffle, J. S., 2010, J. Fluid Mech., 663, 358-384) that included the presence of a magnetic field. The results reveal that the droplet deformation depends on the strength of the magnetic field relative to the background flow and its orientation. Additionally, this work elaborates on the influence of magneto-rheological properties of the fluids on droplet deformation.