Nonlinear Kelvin-Helmholtz instability of a horizontal interface separating two electrified Walters’ B liquids: A new approach

Abstract

The present study scrutinizes the nonlinear stability of a plane interface concerning two fluids of Walters’ B (WB) type. An unchanging tangential electric field (EF) impact upon the two dielectric fluids in the existence of a steady relative velocities. The two fluids have different density viscoelasticity, electrical properties, and in the existence of a surface tension at the interface. The growth implication in engineering and applied physics has motivated the attention of this concern. Due to the difficulty of the mathematical process, the viscoelastic contribution is established only at the interface, which is called the viscous potential flow (VPF). Therefore, the governing equations of motion are analyzed in a linear approach , instantaneously, the nonlinear boundary circumstances (BCs) are provided. This technique creates a nonlinear illustrative equation of the interface displacement. As well-known, the linear stability approach has intensively appeared in several literatures. Consequently, our study focuses only on the nonlinear sense. A new methodology based on the non-perturbative analysis (NPA) is employed to investigate the nonlinear stability and inspect the interface deflection in different situations. The latter equation represents a partial differential equation (PDE) with complex coefficients of the border displacement. Under some restrictions, this equation represents a nonlinear hybrid Rayleigh- Helmholtz oscillator. The considered NPA produces an equivalent linear equation. A numerical methodology is employed to confirm the solutions of the two equations. As well-known, the nondimensional physical numbers are potential to analyze the structures of a fluid flow. Additionally, they reduce the number of variables that describe the system. These quantities frequently have physical meaning which help in some physical interpretations. Therefore, the investigation reveals several non-dimensional physical numerals. The instability benchmarks are theoretically inspected and computationally illustrated through a set of diagrams. The EF strength is strategized against the parameter of the traveling wave number, where the concern of stability/ instability is portrayed. We think that the present analysis is easy, promising, and powerful, and may be applied in diverse contexts.