Damping of capillary waves

Garrett WD, Zisman WA. (1970) Damping of capillary waves on water by monomolecular films of polyorganosyloxanes. JPhysChem74 1796-1805... 

Lucassen Hansen (1966) were one of the first to investigate the damping of capillary waves of surfactant solutions. In Fig. 6.11 their results for n-octanoic acid in 0.005 N HCl and dodecyl amine hydrochloride, both nonionic surfactants, are shown in form of effective dilational elasticity as a fimction of concentration. 

The equation derived for the transport of surfactant ions through the DL describes the adsorption kinetics as a reversible process. The qualitatively new result in the theory of ionic adsorption kinetics is the incorporation of electrostatic retardation for both the adsorption and desorption process, which is of essential importance for processes close to equilibrium. Such a situation exists at harmonically disturbed surfaces, used in investigations of adsorption dynamics like the damping of capillary waves or oscillating bubbles. At sufficiently high frequencies the diffusion layer becomes very thin and the adsorption-desorption exchange is controlled only by the ion transport through the DL, i.e. by the electrostatic retardation. At... 

In the absence of dissipation and with uniform surface tension, plane small-amplitude capillary waves will propagate undamped and unamplified. Viscosity and surface tension gradients lead to the damping of capillary waves. In the following section we shall discuss the damping due to the presence of surface-active substances, which because of the wave shape are not uniformly distributed, giving rise to a spatially nonuniform surface tension. Of interest in... 

For DOC, it can be seen that the results of Williams (1967), for example, show an extra 2.1 g m DOC in the microlayer. If the thickness of the water film obtained with the screen device is taken to be —200 pm, the surface excess of DOC can be calculated as 2.1 X 200 X 10 = 4.2 X 10" g m . A reasonable lower limit to take for the molecular weight of this extra organic material in the surface film is that of a relatively short-chain acid or alcohol with —14 carbon atoms, equivalent to —170 g mole carbon. Using this minimum value, the area per molecule in the ambient type of films sampled by Williams (1967) can be calculated as > — 170/4.2 X lO" X 6.02 X 10 3 = > 70 A. It can be seen from Fig. 1 that for all surface film types except gaseous films, such an area per molecule has no effect on the surface tension of seawater, as measured by the spreading drop method, or on the damping of capillary waves. Moreover, only relatively water-soluble surfactants remain in the gaseous state at film pressures of —10 N m" ... 

Garrett, W.D., 1967a. Damping of capillary waves at the air—sea interface by oceanic surface active material. J. Mar. Res., 25 279—291. 

DAMPING OF CAPILLARY WAVE MOTION BY INSOLUBLE SURFACTANTS... 

Mass transfer across a fluid interface is enhanced by convection in the vicinity of the interface. One source of such convection is wave motion. An increase in the rate of damping of waves can thus be expected to reduce mass transfer rates. As we shall now show, surfactants can cause a significant increase in the damping of capillary waves at a liquid-gas interface. 

Use Equation 5.71 to derive the expressions for damping of capillary waves given by Equations 5.74 and 5.75. Also, find the speed at which waves travel away from the source of vibrations. 

It is direeted from the top, the region of higher surfactant concentration and Iowct surface tension, toward the bottom. Obviously the direction of this force, bring against the direction of Ve, tends to decrease this velocity. When Ve is zero (i.e., e - oo), the surfaee is immobile and IJ - This situation is analogous to the case of an inextensible surfaee considered in the damping of capillary waves in Chapter 5 (Section 3). 

Sloutskin E, Huber P, Wolff M, Ocko BM, Madsen A, Sprung M, Schon V, Baumert J, Deutsch M (2008) Dynamics and critical damping of capillary waves in an ionic liquid. Phys Rev E 77(6). doi 10.1103/PhysRevE.77.060601... 

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