Growth of non-modal transient structures during the spreading of surfactant coated films

Abstract

The spreading of surfactant coated thin liquid films is often accompanied by an instability producing significant film corrugation, fingering and branching. Marangoni stresses, responsible for the rapid and spontaneous spreading, are suspected as the main cause of unstable flow. Traditional eigenvalue analysis of a self-similar solution describing Marangoni driven spreading has predicted only stable modes. We present results of a transient growth study which reveals enormous amplification of initially infinitesimal disturbances in the film thickness. This analysis provides, for the first time, evidence of an instability resembling experimental patterns.