New Methodology for Nonlinear EHD Interfacial Stability Between Two Electrified Viscoelastic Liquids

This work examines a new methodology for the nonlinear electrohydrodynamic interfacial stability of dielectric viscoelastic liquids to enhance the predictive accuracy of microfluidic and biological applications. It tackles the intricacies of nonlinear coupled dynamics, encompassing interfacial deformation and viscoelastic stress influences. This study examines nonlinear stability, as linear stability has previously been thoroughly scrutinized. The interacting fluids are distinguished by differences in density, dielectric permittivity, permeability, viscoelastic parameters, surface tension, and their dynamic response at the perturbed interface. To simplify the mathematical organization, viscous potential flow theory is adopted. Further reduction is achieved by coupling linearized governing partial differential equations with the applicable nonlinear interfacial boundary conditions. This formulation leads to a nonlinear Mathieu oscillator, which governs the evolution of interface displacement. By adopting a non-perturbative approach, the achieved nonlinear ordinary differential equation is transformed into an equivalent linear one. Numerical solutions to the derived stability conditions reveal that the fundamental stability behavior remains qualitatively identical to both the real and complex coefficients associated with nonlinear characteristic equations describing the movement of interfacial displacement. The findings demonstrate that the Darcy number negatively influences the stability region, whereas kinematic viscosities, the Weber number, and Ohnesorge number facilitate the system’s stabilizing impact.