Effective Interfacial Tension Effect on Kelvin-Helmholtz Instability

The instability of the plane interface between two uniform, superposed and streaming Walters′ B′ viscoelastic fluids through porous medium in the presence of effective interfacial tension is considered. The case of two uniform streaming fluids separated by a horizontal boundary is studied. It is observed, for the special case where the effective interfacial tension is ignored, that the system is stable or unstable for the potentially stable configuration which is in contrast to the case of Rivlin-Ericksen viscoelastic fluid or Newtonian fluid where the system is always stable for the potentially stable configuration. Moreover, if the perturbations in the direction of streaming are ignored, then the perturbations transverse to the direction of streaming are found to be unaffected by the presence of streaming, whereas for perturbations in all other directions there exists instability for a certain wave number range. ‘Effective interfacial tension' is able to suppress this Kelvin-Helmholtz instability for small wavelength perturbations, the medium porosity reduces the stability range given in terms of a difference in streaming velocities.