Nonlinear Stability of an Electrified Interface Supporting Surface Charges between Two Viscous Fluids

Nonlinear surface wave instability for electrified Kelvin fluids

“…It is clear that the destabilizing effect of the vertical electric field can be observed through the inspection of conditions (46), (47), and (48). Thus, a vertical field decreases the surface tension (destabilizing effect).…”

“…El-Dib [48] studied the impact of nonlinear and weak viscous effects of interfacial instabilities. In addition, he intended to examine the influence of surface charge density in the presence of a viscous force.…”

Instability for Shearing of an Electrified Kelvin Fluid Sheet with or without Supporting Surface Charges

“…Therefore, condition [37] is replaced by condition [42]. Using the boundary conditions [34]- [36] and [42], the solution of Laplace equation [7] yields another profile for the distribution of the electric potential φ 1 as given in the Appendix. Accordingly, Eq.…”

Electrorheological Kelvin–Helmholtz instability of a fluid sheet

“…The electric conditions that have to be satisfied at y = ±a are condition (20) and condition (21). With these boundary conditions, the solution of the Laplace equation (28) yields the distribution of the potential field φ 1 in the three layers, as given in Appendix A.…”

“…Furthermore, the viscosity affects the surface charge density. El-Dib [21] has extended the nonlinear stability of charged interfaces between two inviscid fluids studied by Mohamed and Elshehawey [22] in order to study the impact of the relation between the viscosity force and the surface charges density through nonlinear analysis of viscous flow. He considered the same approach for weak viscous forces, as demonstrated in [19].…”