Instability and breakup of a magnetic fluid jet in a solenoid field

Background. Magnetic fluids are synthesized artificially by colloidally dissolving of solid ferromagnetic's nanoparticle in a usual non-magnetic fluid. Having the magnetization ability, such fluids interact with an applied magnetic field capable of affecting their motion. A wide variety of practical applications of magnetic fluids in various fields of engineering and technology is based on this fact. The study formulates a mathematical model of waves propagation and instability of waves on the surface of a magnetic fluid jet that is situated in a magnetic field of a coaxial solenoid. Materials and methods. The authors used the methods of mathematical physics and solved the problem in a cylindrical coordinate system ($r, \theta, z$). The dispersion equation was investigated by numerical methods. Results. A mathematical model of propagation and instability of waves on the surface of a magnetic fluid jet in a solenoid magnetic field was formulated and investigated. The full solution of the boundary value problem for hydrodynamic and magnetic quantities was found. The numerical analysis of the dispersion equation was completed. It is shown that the magnetic field has a stabilizing effect on jet's motion. Conclusions. The size of droplets, occurring during fragmentation of the fluid jet, increases with the growth of the magnetic field, while the droplets growth rate and appearance frequency decrease.