Author(s)

L. Likhterov

Abstract

Fluctuations of an insoluble surfactant monolayer along the free liquid surface induced by standing waves are considered theoretically. The energy of the fluctuating interface is assumed to be equal to the total free energy that is a function of surface tension. The dependence of the surface concentration on the surface tension is taken according to the Gibbs adsorption equation. Van der Waals forces between molecules that are present in all condensed matter systems are taken into account in the form of van der Waals energy for a thin film. The obtained theoretical result shows that the longitudinal distribution of the surfactant concentration can be expressed analytically, and that the distribution of concentration changes relative to some reference level has been found to be periodic with a period that is half of the wave period. The maximal concentration is achieved in nodal points of the wave profile. 1 Introduction Wave motions in small-scale systems may be useful for transport of insoluble, film forming surfactant molecules floating on the free liquid surface. Surfaceactive agents (surfactants) are used for decreasing surface tension and also for laminarization and hydrophobization of flows having complex structures. The dynamics of localized surfactant on a thin film has been considered by Gaver and Grotberg [1], who employed the lubrication theory to derive equations that describe the evolution of the film thickness and surfactant concentration. Numerical investigation of patterns of standing waves has been performed by Dolnik et al. [2], who obtained the different wave patterns associated with the aperiodic instability in a two-dimensional reaction-diffusion model. Their results

Keywords