Effect of magnetic fields on the capillary instability of an annular liquid jet

Abstract

The hydromagnetic stability of an annular liquid jet is presented analytically; the results are confirmed numerically and interpreted physically. A general eigenvalue relation describing the (in-) stability characteristics of that model is derived, using the linear perturbation technique. In the absence of the magnetic field, the model is absolutely unstable only to axisymmetric perturbations whose wavelength is longer than the circumference 2π R of the gas-core jet; and stable to all other perturbations. The magnetic field has a strong stabilizing influence to all modes of perturbation for all wavelengths. Its effect is to decrease the wavelength at which the capillary instability occurs. The latter is completely suppressed by a magnetic field strength greater than ( T 2gmR ) 1 2 (where T and μ are the surface tension and magnetic permeability coefficients) and then the stability arises. The capillary instability remains unaffected by magnetic field effects in the longitudinal symmetric motions. The present results with zero magnetic fields are in good agreement with Kendall's experimental results (1986).