An Analysis of the Effect of Surfactant on the Leveling Behavior of a Thin Liquid Coating Layer

A linear analysis, employing the lubrication approximation, is presented for the leveling history of a thin layer of Newtonian liquid. When the surface tension is taken to be constant, the classic result of Orchard is reproduced. As expected, the presence of surfactant, with resulting surface-tension-gradient forces, slows the rate of leveling of an initial train of periodic ripples. For very weak surfactants, initial leveling rates are unaffected, but ripple amplitude can be lowered only to a “plateau” level which persists for long times. Surprisingly, critical surfactant concentrations exist, depending on other system parameters such as the coating thickness and ripple wavelength, for which leveling is maximally retarded. To the extent that this retardation is generally undesirable, it is suggested that these critical values be avoided, even by increasing the amount of surfactant present. This anomalous effect is maximized for an assumed nondiffusing, insoluble surfactant and is mitigated by either surface or bulk diffusion of surfactant.