Stability of Two Superposed Rivlin-Ericksen Viscoelastic Dusty Fluids in the Presence of Magnetic Field
The stability of the plane interface separating two Rivlin-Ericksen viscoelastic superposed fluids permeated with suspended particles and uniform horizontal magnetic field is considered following the linearized perturbation theory and normal mode analysis. The stability analysis has been carried out, for mathematical simplicity, for two highly viscoelastic fluids of equal kinematic viscosities and equal kinematic viscoelasticities. For potentially
stable configuration, the system is found to be stable for
disturbances of all wave numbers. The magnetic field succeeds in stabilizing certain wave-number range, for the potentially unstable configuration. The case of exponentially varying density, viscosity, viscoelasticity, magnetic field and particle number density is also
considered. For stable density stratification, the system is found to be stable for disturbances of all wave numbers. The magnetic field succeeds in stabilizing the potentially unstable stratifications for a certain wave-number range which were unstable in the absence of the magnetic field. Discussion of oscillatory modes and non-oscillatory modes are also made.
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