Applied Sciences Department, College of Technological Studies, PAAET, Kuwait
Mathematics Department, Faculty of Science, Helwan University, Egypt
This study aims to discuss and illustrate the role of insoluble surfactants on the stability analysis of a shear-imposed free surface motion down an oblique heated substrate. The couple effects of temperature and surfactant concentration gradient on the surface tension are assessed, in which the surface tension of the fluid is assumed to vary linearly on surfactant concentration and the temperature. The exact analytical solutions for the Stokes flow and the long-wave approximation are derived, depending on the linear stability theory, and hence the neutral curves are plotted and discussed. Due to the presence of the surfactant, there are two different modes that impact the stability process of a shear-imposed inclined flow. The current study recovers some limiting cases upon the selected data. The system parameters governing the liquid layer and the substrate geometry have a strong effect on the wave forms and so the stability of the free surface. The influences of various parameters such as Marangoni, Biot, elasticity, surfactant Péclet number and Reynolds numbers, besides the angle of inclination are considered. It is found that, the Reynolds and the surfactant Péclet numbers and the angle of inclination have destabilizing effects.