For this last case, a cylindrical structure, which can be a wire, is necessary at the ferrofluid cylinder center to overcome a singularity. The magnetic fields admitted by these assumptions can be divided into two groups: axial and non-axial magnetic fields. A linear stability analysis of this system is realised by imposing a small amplitude axisymmetric disturbance. The ferrofluid is placed under isothermal conditions with no gravity. This theoretical study on ferrofluid jets is supported by LabEx through the INFEMA (INstabilities of FErrofluid flows in MAgnetic fields) project common between the two Norman laboratories CORIA (UMR 6614) and LOMC (UMR 6294 – Le Havre).Īn incompressible Newtonian ferrofluid cylinder under a steady axisymmetric magnetic field is considered. However, ferrofluids can have a viscosity one order of magnitude higher than the one of water and it must be taken into account. These ones are focused on particular magnetic field shapes with inviscid ferrofluids. In the literature, many temporal stability analysis of ferrofluid cylinders under a magnetic field are identified. Nevertheless, for sufficiently high jet velocities, the temporal stability analysis of an infinite length cylinder allows to retrieve the main characteristics of the jet instability. Because the instability is developing along the axis of the jet, a spatial stability analysis is required. In order to predict the behaviours of ferrofluid jets, especially the breakup into drops, a stability analysis can be realised. This is the case, for example, in the printing field where the magnetic ink is shifted towards a surface, and in medicine where the drug carried by the ferrofluid is directed towards the place to cure, thanks to a magnetic field. These jets and these drops are controlled with the help of a magnetic field. Ferrofluids are used in many fields, frequently under the form of jets and drops. They are obtained by dispersing nanoparticles of magnetite into a liquid phase and by incorporating a surfactant to prevent the agglomeration of the particles. Because ferromagnetic materials lose their magnetic properties at liquid state, ferrofluids need to be synthesized. Ferrofluids are liquids exhibiting strong magnetic properties.
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