Stability of a localized heated falling film with insoluble surfactants

In this paper, we investigated a liquid film uniformly covered by insoluble surfactants flowing over a local heater. The lubrication approximation was applied to derive two coupled nonlinear evolution equations governing the thickness of the liquid layer and the surfactant concentration. Influences of surfactant on the base state were studied and linear stability analysis was carried out to investigate the surfactant’s effectiveness on the stability of the base state. Results of linear stability analysis showed that surfactant had dual effects. The system became more stable as the surfactant concentration increased; while it became more unstable as diffusion of the surfactant increased. The nonlinear time evolution study was carried out to examine the linear stability analysis.