Magnetic field-induced control of a compound ferrofluid droplet deformation and breakup in shear flow using a hybrid lattice Boltzmann-finite difference method

The deformation and breakup dynamics of a compound ferrofluid droplet under shear flow and uniform magnetic field are numerically studied in this paper. Utilizing magnetic field provides the possibility to obtain better control over the compound droplet morphology and breakup in a simple shear flow. To solve the governing equations for interfaces motion and hydrodynamics, the conservative phase field lattice Boltzmann model is employed, and a finite difference approach is applied for calculating the magnetic field. To verify the accuracy of present simulations, the results are validated with those of four relevant benchmarks including liquid lens between two stratified fluids, three-phase morphology diagram, droplet under simple shear flow fluid flow, and ferrofluid droplet elongation under a uniform magnetic field. The magnetic field lines and magnetic force in the presence of ferrofluid are visualized. The effects of capillary and magnetic Bond numbers on the deformation and inclination angle of compound droplet under magnetic field at the angles of 45∘ and 135∘ are investigated when the inner or outer droplet is ferrofluid. The results show that by increasing capillary number, the shear force becomes greater and deforms the outer interface, whereas its effect on the inner interface is negligible and its small deformation is due to the squeezing force by the outer interface. As the magnetic Bond number increases, so does the magnetic force, and it leads to both of inner and outer interfaces elongation in the direction of the imposed magnetic field. Finally, the regime maps of compound droplet morphology and breakup in terms of capillary and magnetic Bond numbers are presented when the outer droplet is ferrofluid and the magnetic field is applied at the directions of 45∘ and 135∘, respectively. The border between breakup and non-breakup regions is illustrated, and according to the equilibrium shape of the compound droplet, donut-shaped, egg-shaped, eye-shaped, and peach-shaped regimes are observed in the non-breakup region. •A compound ferrofluid droplet under shear flow and a uniform magnetic field is studied.•A hybrid lattice Boltzmann-finite difference model is utilized.•The accuracy of the results is validated with four relevant benchmarks.•The effects of magnetic Bond and capillary numbers on the droplet deformation are studied.•The regime maps of a compound ferrofluid droplet morphology and breakup are presented.