A laboratory study of longitudinal waves in surfactant films in a water wave tank

Abstract

The dynamics of longitudinal surface waves in surfactant films in a large wave tank (14.8 m long, 1.2 m wide, and 1.0 m deep) were studied experimentally. Three soluble surfactants (Triton X‐100, sodium dodecyl sulfate, and hemicyanine) were added to the tank water in separated experiments; however, other naturally occurring surfactants were present as well. Since it is exceedingly difficult to control surfactants in large water tanks, these mixed surfactant conditions are probably typical of laboratory‐scale experiments on the effects of surfactants on gravity‐capillary wave phenomena. In the present experiments, longitudinal waves were generated with a Teflon bar that barely touched the water surface and oscillated horizontally in a direction perpendicular to its length. The longitudinal waves were measured with a technique that is based on the phase shift of capillary waves that were generated mechanically with a propagation direction perpendicular to that of the longitudinal waves. The wave number (αL), the phase speed, and the damping coefficient (βL) of the longitudinal waves were obtained for wave frequencies ranging from 0.2 to 1.5 Hz in the various surfactant films. The experimental data agree well with the theoretical dispersion relationship of longitudinal waves, and the fitting of this equation to the experimental data yielded the equilibrium surface elasticity, the surface viscosity, and the surface‐to‐bulk diffusion parameter. For nearly all experimental conditions, βL/αL was greater than 0.414, its value based on theory with the surface viscosity set to zero. It was found that the longitudinal wave dispersion curves intersect the capillary‐gravity wave dispersion curves at frequencies ranging from 2.53 to 3.55 Hz. This intersection point is known to be the frequency of the maximum damping of capillary‐gravity waves.