Abstract
Derived in this paper are evolution equations for the thickness and surface surfactant concentration pertaining to a thin liquid layer that is laden with a soluble surfactant as it flows under the influence of gravity down a heated incline. These equations account for variations in surface tension with surfactant concentration and temperature. A linear stability analysis and numerical simulations are carried out and discussed. An expression for the critical Reynolds number has been obtained and includes both thermocapillary and solutocapillary effects. The linear stability analysis was found to be in harmony with the nonlinear numerical simulations. A comparison with a weighted residual model also revealed good agreement.
Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
