Impact of Vertical Magnetic Field on the Rivlin-Ericksen Fluid Interface: An Irrotational Flow Approach

This study explores the influence of a magnetic field that is perpendicular to the interface on the Rayleigh-Taylor instability. The analysis focuses on electrically conducting and incompressible fluids, specifically a viscoelastic liquid in the upper region and a viscous fluid in the lower region. To investigate the problem, the irrotational flow theory is used, which accounts for viscosity through normal stress balance and does not consider tangential stresses or impose no-slip conditions at the rigid boundaries. Using Rivlin-Ericksen’s model for the viscoelastic liquid, a second-order dispersion relation is derived and numerically analyzed to determine the growth rate of the instability. Several plots are generated using the dispersion relation, and the stability of the interface is discussed for various physical parameters. The study reveals that the inertial forces contribute to the instability of the interface, while surface forces tend to stabilize it.