On the flow-induced Marangoni instability due to the presence of surfactant

Abstract

The flow-induced Marangoni instability due to the presence of surfactant is examined for long-wavelength perturbations. A unified view of the underlying mechanisms is provided through revisiting both falling film and two-fluid Couette flow systems. The analysisis performed by inspecting the corresponding coupled set of evolution equations for the interface and surfactant concentration perturbations. While both systems appear to have very similar sets of equations consisting of base flows and Marangoni effects, the origins of stability/instability are identified and illustrated from a viewpoint of vorticity. The base flow rearranges the surfactant distribution and the induced Marangoni flow tends to stimulate the interface's growth. But this destabilizing effect is reduced by effects combining the interface travelling motions and the Marangoni recoil. The competition between these opposing effects determines the system stability, and is elucidated using equations in concert with observations from initial value problems. Moreover,a criterion for the onset of instability can be established in line with the same rationale. The present work not only furnishes a lucid way to clarify the instability mechanisms, but also complements previous studies. Extension to the weakly nonlinear regime is also discussed.