Abstract
A theory is formulated to describe the dynamics of a thin film flowing down an inclined plane laden with insoluble surfactant, present in dilute concentrations. Use of lubrication theory yields a coupled pair of partial differential equations for the film height and surfactant monolayer concentration. The contact line singularity is relieved by assuming the presence of a thin precursor layer ahead of the advancing film. Base flow solutions for a flow of constant flux are examined over various inclination angle, precursor-layer thickness, Peclet number, and capillary parameter ranges. Application of a transient growth analysis highlights the presence of an instability and the vulnerability of the flow to transverse disturbances of intermediate wavenumber. Our results reveal that several key features of the much-studied uncontaminated film flow, including stability, are modified qualitatively by the inclusion of surfactant.
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