A new methodology in evaluating nonlinear electrohydrodynamic azimuthal stability between two dusty viscous fluids

Abstract

The objective of the current paper is to scrutinize the azimuthal stability of a circular interface between two viscous fluids across porous medium in the presence of fine dust. Dusty fluid models are employed to comprehend the dynamics of aerosols in the atmosphere, a crucial aspect in the investigation of air quality, climate change, and the dissemination of pollutants. Furthermore, the comprehension and management of azimuthal nonlinear instabilities are essential in diverse engineering applications, where turbulence is a prominent factor. This includes aerospace engineering, where it is necessary for developing more efficient aircraft, as well as fluid dynamics, where it is critical for optimizing industrial processes. The system is subjected to the influence of a uniform electric field (EF) that is directed in the azimuthal direction. Electrospray trustees utilized in spaceship propulsion systems make use of the principles of Electrohydrodynamics (EHD). These representatives employ the process of ionization on a liquid propellant and utilize EFs to accelerate the resulting ions, so producing thrust. Assuming a simplified situation, the prototype is assumed to have a two-dimensional structure. Both fluids are presumed as rotating. An examination of rotating fluids is crucial for comprehending the dynamics of the atmosphere and oceans. Obtaining this knowledge is essential for accurately predicting weather, simulating climate patterns, and investigating oceanic currents. The mathematical approach is simplified by considering the viscous potential theory (VPT). The nonlinear technique relies on the use of linear fundamental partial differential equations (PDEs) and the application of the appropriate nonlinear boundary conditions (BCs). This method produces a nonlinear PDE that controls the displacement of the interface. By disregarding the nonlinear elements, a dispersion equation that is linear in nature is obtained. The stability criteria are graphed using several dimensionless physical quantities. The non-perturbative analysis (NPA) achieves nonlinear stability. As well-known, the primary objective of NPA is to convert a linear ordinary differential equation (ODE) into a linear equation. The NPA distinguishes itself from conventional perturbation methods by its ability to accurately analyze the dynamics of highly nonlinear oscillators. This novel methodology is developed utilizing the He's frequency formula (HFF) for the purpose of designing the displacement of the interface. The computational computations demonstrated that the NPA is efficacious, encouraging, and powerful. The linear and nonlinear techniques demonstrate that the effects of various dimensionless physical parameters remain constant. It is found that the Weber number We and Capillary number Cabecome zero as crucial consequences. The Ohnesorge number, Oh which represents the ratio of viscosity and the mass concentration in dusty particles, has a destabilizing effect.