Long-Wavelength Marangoni Convection in a Liquid Layer with Insoluble Surfactant: Linear Theory

Abstract

The subject of this paper is the long-wave Marangoni convection in a horizontal liquid layer with insoluble surfactant absorbed on the free surface. The surfactant is convected by interfacial velocity field and diffuses over the interface but not into the bulk of the fluid. The layer is subjected to a transverse temperature gradient. The buoyancy effects are negligible as compared to the Marangoni forces. We consider both cases of flat nondeformable and deformable surface. The linear stability analysis of this system is performed. It is shown that in both cases of the upper surface monotonic and oscillatory modes exist. Convection thresholds are determined and the critical Marangoni numbers for monotonic as well as for oscillatory mode are obtained. It is shown that the monotonic long-wave instability is more dangerous than oscillatory one only for small elasticity numbers, if the Lewis number is small.