Electrohydrodynamic Stability of Walters B′ Viscoelastic Dielectric Liquid Jet Streaming with Variable Velocity into Another Viscoelastic Fluid via Porous Medium (European Journal of Pure and Applied Mathematics, 2025)
A linear axisymmetric instability analysis of a streaming Walters B′ viscoelastic liquid jet with a parabolic velocity profile surrounded by viscoelastic fluid under the impact of an axial electric field via porous media is investigated in the Rayleigh and atomization modes. Only temporal instability is considered because, due to the large Weber number, both temporal and spatial instability give almost the same outcomes in the atomization regime. The dispersion relation is calculated to evaluate the growth rate of disturbances. The findings of stability analysis show that the viscoelastic parameters, electric field, velocity profile parameter, and porosity of the porous medium hinder instability for both Rayleigh and atomization modes, while the density ratio, dielectric constants, and kinematic viscosities enhance instability in both modes. Weber number hinders instability in Rayleigh mode, but it enhances instability in atomization mode. The effects of all parameters in atomization mode are found to be more unstable than those in Rayleigh mode. It is also demonstrated that the Walters B′ viscoelastic liquid jet is more stable than an inviscid liquid jet, and the breakup process in the atomization mode of instability occurs faster than in Rayleigh mode since liquid jet instability is closely related to drop formation and breakup.
Keywords: Linear stability; Viscoelastic liquid jet; Linear stability; Electrohydrodynamics