Schwartz LW, Cairncross RA, Weidner DE

Abstract:

Our recently-published linear analysis [Schwartz et al., Langmuir 11, 3690 (1995)] demonstrated that an initially rippled thin layer of Newtonian liquid with uniformly distributed surfactant may level in unexpected ways. While the presence of surfactant will, in general, slow the rate of leveling compared to that of a perfectly clean system, there was shown to exist a realistic parameter range where increasing, rather than reducing, the amount of surfactant present will hasten leveling. Here, for the two-dimensional problem, we investigate the importance of nonlinearity though numerical solution of (i) the unsteady lubrication form of the evolution equations with surfactant, and (ii) finite-element solution of the exact governing equations for slow viscous flow. Confirmation of the linear results is demonstrated and quantitative discrepancy only appears for large-amplitude and short-wavelength ripples. Surface tension gradient driven flow explains the anomalies; for moderate surfactants, the surface quickly 'hardens,' leading to a decay rate of one-quarter of the clean-surface rate, while for weak surfactants, leveling proceeds to a plateau level which decays much slower than the hard-surface result.