Distribution Of Surfactant Along The Free Liquid
Surface Under The Action Of Surface Waves
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
Related Book
Other papers in this volume
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