Partial Differential Equations in Applied Mathematics (Jun 2024)
Nonlinear stability of two superimposed electrified dusty fluids of type Rivlin-Ericksen: Non-perturbative approach
Abstract
The nonlinear instability of a planar interface between two overlapping Rivlin-Ericksen viscoelastic liquids, in the occurrence of fine dust and vertical electric fields throughout permeable media, and the influence of surface tension is studied. The prototype structure is assumed to be a two-dimensional groundwork for the sake of simplicity. The growing approval of several disciplines of practical physics and technology serves as motivation for analyzing this problem. Using viscous potential theory, the mathematical procedure is condensed. To properly control electro convection in liquid crystals, which is widely used in various displays technologies, it was crucial to have a thorough comprehension of stability. Gaining understanding of the behavior of viscoelastic fluids at interfaces was crucial in polymer manufacturing industries. Employing the linear equations of movement with the suitable nonlinear bounder circumstances forms the basis of the considered nonlinear technique. A nonlinear partial differential equation that evaluates the interface movement is the objective of the process. Since linear stability has frequently been investigated, the present situation will be constructed only in the nonlinear sense, where a number of dimensionless physical numerals are achieved. The non-perturbative methodology is used to accomplish the nonlinear standards. The main idea behind the novel performance is to convert an ordinary nonlinear ordinary differential equation into a linear one. The new technique differs from the conventional perturbation methods in that it may be used to exactly and correctly analyze the behavior of the strong nonlinear aspects of the interface displacement. This innovative method is established by using He's frequency formula. Using the nonlinear distinguishing equation, the special situation of the real and the complex coefficients is accomplished. It was observed that the instability zone expands as the electric field, porosity of porous medium, and density ratio of two fluids rise. The stability configuration is enhanced by the viscoelasticity parameter, Bond number, and ratio of kinematic viscoelasticity.
