The magnetohydrodynamic (MHD) stability of streaming of liquid cylinder with doubly perturbed interfaces coaxial with a streaming fluid mantle jet has been developed. A general dispersion relation is derived, discussed and some reported works are described. The analytical results are confirmed numerically and interpreted physically. The streaming is purely destabilizing while the capillary force is such as for small axisymmetric perturbations only. The magnetic field has a strong stabilizing influence and it gives a measure of rigidity in the fluids. The radii (liquid-fluid ) ratio plays an essential role in increasing the MHD stabilizing domains. The densities (liquid-fluid) ratio have a very small stabilizing effect. If the magnetic field strength is so strong that the Alfen wave velocity is much greater than the streaming speed, the capillary and streaming destabilizing character is completely suppressed and stability sets in. The present results are in good agreement with the experimental results of Kendall (1986) since we neglect here both the magnetic field influence and the inertia force of the interior fluid jet.
The present work extends Chandrasekhar's theory CHANDRASEKHAR [2] of axisymmetric capillary instability of a hollow jet. Here the instability of this model is investigated for all (non)-axisymmetric perturbation modes under the combined effect of the capillary and electrification forces. The electrification dispersion relation has been derived, studied analytically and numerically, and the (un-) stable domains are identified. Some reported results are recovered as limiting cases. The principle of the exchange of instability is valid. The capillary instability of a hollow jet becomes worse in the presence of the electrification forces.