  Surfactant-laden thin liquid films overlaid on solid substrates are
encountered in a variety of industrial and biological settings. As these films
reach submicron thickness, they tend to become unstable owing to the influence
of long-range dispersion forces. In the current study, we investigate how
gravitational drainage affects the stability attributes of such thin liquid
films. Using scaling arguments, we demonstrate that gravity and dispersion
forces can exert their influence simultaneously over a wide range of film
thicknesses. In the lubrication limit, we carry out linear stability analysis
and nonlinear simulations to understand the evolution of draining thin films.
Linear stability indicates the existence of two unstable modes and two cut-off
wavenumbers, as opposed to a single unstable mode and a unique cut-off
wavenumber observed in stationary films. It is also found that surfactant-laden
flowing films are more stable than stationary films with surfactants as well as
draining films with clean interfaces. The origin of stabilization is identified
as the enhanced surfactant perturbations generated due to drainage. We
demonstrate that films exhibiting intermediate levels of surfactant activity
and significant drainage exhibit the lowest rates of disturbance growth,
leading to extending the time of rupture.
