Fingering phenomena associated with insoluble surfactant spreading on thin liquid films

Abstract

We study the linear and nonlinear stability of a thick surfactant deposition spreading on a thin liquid film using transient growth analysis (TGA) and direct numerical simulations (DNS) of the two-dimensional lubrication equations, respectively. Results of the TGA of the one-dimensional spatially and temporally evolving base state reveal disturbance growth and the selection of a perturbation of intermediate wavenumber. This perturbation targets the ‘contact region’ between the deposition and the underlying thin liquid film and grows despite the absence of intermolecular forces. Increasing the initial thickness ratio of the deposition to the thin film and decreasing the relative magnitude of capillarity and surface diffusion further amplify perturbation growth. The DNS results clearly show the formation of fingers in the contact region behind the surfactant leading edge and provide further confirmation of the TGA findings.