An ISPH–FVM coupling method for simulation of ferrofluid droplet deformation in shear flow under a uniform magnetic field

The dynamic behavior of ferrofluid droplets under shear flow and a uniform magnetic field is numerically investigated by the ISPH-FVM (incompressible smoothed particle hydrodynamics-finite volume method) coupling method. In this method, ISPH particles are utilized to track the motion of the ferrofluid interface, while the background fluid is defined on the grid. To describe the influence of the magnetic field in the computational domain, a magnetic force is introduced into the ISPH-FVM coupling method as the interface force. To verify the accuracy of the magnetic force model in the ISPH-FVM coupling method, the deformation of 2D/3D ferrofluid droplets under a uniform magnetic field is first simulated. Next, the deformation behavior of ferrofluid droplets under a shear flow field and a uniform magnetic field is simulated, and it is found that the orientation angle of the droplet is greatly influenced by the shear rate while the deformation ratio is greatly influenced by the magnetic field intensity. Furthermore, the collision behavior of two droplets under shear flow and a uniform magnetic field is further explored. It is shown that with an increase in the capillary number, two ferrofluid droplets will not merge after collision without an external magnetic field. Finally, the dynamic behavior of a compound droplet under shear flow and a magnetic field is predicted by the present coupling method. The numerical examples demonstrated that the ISPH-FVM coupling method can well predict the interface behavior of ferrofluid droplets under shear flow and a uniform magnetic field.