S. A. Alkharashi - Applied Sciences Department, College of Technological Studies, PAAET, Kuwait
A. Assaf - Mathematics Department, Faculty of Science, Helwan University, Egypt
K. Al-Hamad - Applied Sciences Department, College of Technological Studies, PAAET, Kuwait
A. Alrashidi - Applied Sciences Department, College of Technological Studies, PAAET, Kuwait

The purpose of this study is to establish the effects of insoluble surfactants on the stability of two layers flow down an inclined wall in the limit of Stokes and long-wavelength approximations. The dynamics of the liquid-liquid interface is described for arbitrary amplitudes by evolution equations derived from the basic hydrodynamic equations, in which the fluids are subjected to a uniform electric field. The principle aim of this work is to investigate the interfacial stability as well as the growth rate in the presence of insoluble surfactants. The parameters governing the flow system, such as Marangoni, Weber, capillary numbers and the inclined substrate strongly affect the waveforms and their amplitudes and hence the stability of the fluid. Approximate solutions of this system of linear evolution equations are performed. epending on the selected parameters, the phenomenon of the dual role is found with respect to the electric Weber number as well as the viscosity ratio. The interfacial waves will be more stable due to the growth of the Marangoni number while, while the opposite effect is found for the increase in capillary number. In the longwave perturbations, the stability process is found to confirm the stabilizing effect of the Marangoni number and the destabilizing influence of both capillary and Reynolds numbers, whereas the dual role is observed for the dielectric ratio.

Inclined substrate, Insoluble surfactants, Viscous fluids, Long wave analysis, Electric field