BREAKUP OF A CYLINDRICAL COLUMN OF MAGNETIC
FLUID WITH A NON-HOMOGENEOUS POROUS CORE 

Taktarov Nikolai Grigoryevich, Doctor of physical and mathematical sciences, professor, sub-department of mathematics, Mordovia State Pedagogical Institute named after M. E. Evsevyev (11a Studencheskaya street, Saransk, Russia), colonnt@mail.ru
Runova Olga Alexandrovna, Postgraduate student, Mordovia State Pedagogical Institute named after M. E. Evsevyev (11a Studencheskaya street, Saransk, Russia), runova.olga@list.ru

533.9:537.84

Background. The magnetic fluids, not existing in nature, are synthesised artificially by means of dispersion of nanoparticles of solid ferromagnetic in the usual non-magnetic fluid. The magnetic fluids have found a broad application in different areas of technology. A mathematical model of waves propagation and instability on a surface of a cylindrical column of magnetic fluid of infinite length, surrounding a coaxial infinite long non-homogeneous (laminated) porous core of round section was constructed and studied.
Materials and methods. The authors used the methods of mathematical physics and solved the problem in a cylindrical coordinate system . The presence of the surface tension was taken into account. The gravity was neglected.
Results. The equations of motion of the magnetic fluids inside and outside of the porous medium and the equations for the magnetic field were written. The boundary conditions for hydrodynamic and magnetic quantities on interfaces of the mediums were formulated. The full solution of a boundary value problem for hydrodynamic and magnetic quantities was found. The numerical analysis of the dispersion equation that describes surface wave propagation was completed. The authors found the conditions, under which the disturbances of the fluid column surface become unstable and result in its fragmentation into a chain of connected droplets.
Conclusions. The size of droplets, occurring during fragmentation of the fluid column, increases with the growth of the magnetic field, i.e. magnetic field has a stabilizing effect on the fragmentation of the fluid column.

surface waves, instability, magnetic fluid, porous medium, magnetic field.

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