EHD Instability Modes of Power-Law Fluid Jet Issuing in Gaseous Streaming via Permeable Media

The instability of a non-Newtonian dielectric fluid jet of power-law (P-L) type injected when streaming dielectric gas through porous media is examined using electrohydrodynamic (EHD) linear analysis. The interfacial boundary conditions (BCs) are used to derive the dispersion relation for both shear-thinning (s-thin) and shear-thickening (s-thick) fluids. A detailed discussion is outlined on the impact of dimensionless flow parameters. The findings show that jet breakup can be categorized into two instability modes: Rayleigh (RM) and Taylor (TM), respectively. For both fluids, the system in TM is found to be more unstable than that found in RM, and, for s-thick fluids, it is more unstable. For all P-L index values, the system is more unstable if a porous material exists than when it does not. It is demonstrated that the generalized Reynolds number (Re_n), Reynolds number (Re), P-L index, dielectric constants, gas-to-liquid density, and viscosity ratios have destabilizing influences; moreover, the Weber number (We), electric field (EF), porosity, and permeability of the porous medium have a stabilizing impact. Depending on whether its value is less or more than one, the velocity ratio plays two different roles in stability, and the breakup length and size of P-L fluids are connected to the maximal growth level and the instability range in both modes.