Longitudinal capillary waves. Part 1.—Theory

Abstract

The existence of hitherto unobserved surface waves with a longitudinal character is deduced theoretically and the properties of these waves are predicted. In contrast to capillary waves, the longitudinal waves are governed by the surface elastic modulus rather than by surface tension ; they are accompanied by a horizontal rather than by a vertical surface movement and they are connected with a liquid flow of a highly dissipative character causing a rapid damping. Under normal experimental conditions capillary waves and longitudinal waves are superimposed, but the longitudinal wave is usually damped out much more rapidly, except at high elastic modulus.

Theory and experiment on resonant frequencies of liquid-air interfaces trapped in microfluidic devices

“…32 Bond number, 19 the ratio of buoyancy forces and surface tension forces, was found to be of the order of 10 À4 for the horseshoe-shaped structures employed. Hence, we neglected the effect of gravity on fluid motion.…”

“…[13][14][15][16][17] Although analysis of the trapped-bubble, i.e., liquid-gas interface, has not been attempted, extensive analysis of unbounded liquid-gas and liquid-liquid interfaces has been performed. [17][18][19][20][21][22] In the case of bounded interfaces, formulation of a liquid-liquid interface has been developed. [23][24][25] Attempts have also been made to analyze a cylindricalshaped liquid-gas interface trapped over rectangular shapes.…”

Evidence for two-dimensional solitary sound waves in a lipid controlled interface and its implications for biological signalling

“…0. This has direct implications for capillary (transversal) modes which scale with g and are therefore almost unavoidable in monolayers but are likely to be absent in a bilayer [16,34]. Excitation of longitudinal waves is therefore expected to be more efficient in lipid bilayers.…”

Surface Waves at the Interface Between two Viscous Fluids

“…The fluid was taken as incompressible but there is still a component of velocity on y-direction. As far as we know, nobody has ever pointed out this fact clear, except Lucassen in his works [7][8][9][10], who considered incompressible fluids, but the movement in y-axis was due to active materials on the surface, no as an effect of viscosity. This coupling of movements could be responsible for a less wavelength and a bigger dissipation as it will be seen later.…”