Characterization of capillary waves: A review and a new optical method

Abstract

The methods to study capillary waves have been reviewed together with the emerging practical applications of theirs and new theoretical developments in the field. The focus is on monochromatic ripples of frequency in the range 0.1–10 kHz. A capillary wave apparatus has been constructed that combines several recent advances on the technique. It is based on the profilometry of waves decaying with distance, with a high-speed video camera detecting the light refracted by the surface. A code to process the images has been developed, which executes a regression analysis to determine the characteristics of the wave. High precision and accuracy have been achieved: standard deviation from the mean of ±0.5% for the wavelength and ±7% for the decay length; mean deviations from the theoretical values ±0.2% for the wavelength and ±5% for the decay length. An analytic approximation for the dispersion relation has been used to determine the Gibbs elasticity of a surfactant monolayer from the data for decay length vs frequency. The elasticity of an octanol monolayer has been determined with precision of ±1 mN/m, in excellent agreement with the theoretical value. Surface tension can be measured from the wavelength data with precision of ±0.3 mN/m. It has been demonstrated that the effect of the surface elasticity on the wavelength is significant, and accurate wavelength data can actually be used to determine the elasticity if the surface tension is known.