Wave damping

Fig. IV-10. Wave-damping behavior of polydimethylsiloxane heptadecamer on water at 25°C at (a) 60 cps and (b) 150 cps. Curve (c) gives the ir-

Viscosity, defined as the resistance of a liquid to flow under an applied stress, is not only a property of bulk liquids but of interfacial systems as well. The viscosity of an insoluble monolayer in a fluid-like state may be measured quantitatively by the viscous traction method (Manheimer and Schechter, 1970), wave-damping (Langmuir and Schaefer, 1937), dynamic light scattering (Sauer et al, 1988) or surface canal viscometry (Harkins and Kirkwood, 1938 Washburn and Wakeham, 1938). Of these, the last is the most sensitive and experimentally feasible, and allows for the determination of Newtonian versus non-Newtonian shear flow. 

It is evident that the standing pressure wave in a rocket motor is suppressed by solid particles in the free volume of the combushon chamber. The effect of the pressure wave damping is dependent on the concentrahon of the solid parhcles, and the size of the parhcles is determined by the nature of the pressure wave, such as the frequency of the oscillation and the pressure level, as well as the properties of the combustion gases. Fig. 13.25 shows the results of combustion tests to determine the effechve mass fraction of A1 parhcles. When the propellant grain without A1 particles is burned, there is breakdown due to the combushon instability. When... 

If the concentration of added surface-active agent is varied, one often finds that the extraction rate passes through a shallow minimum (between 30% and 40% of the value with no additive) 72). Where this occurs, the concentration of surface-active agent is usually of the order 10 mAf to ImM. This may be related to the similar maximum found for wave-damping at a certain concentration of surface-active agent 1, 30). 

Emmert and Pigford (E4), Ternovskaya and Belopol skil (T9-T12), and Tailby and Portalski (T3) have carried out detailed investigations of the effects of surfactants, using several different surfactants, each at a number of concentrations. In nearly all cases it was found that, as the concentration of surfactant was increased, the waves were rapidly damped out as far as some optimum concentration, beyond which there was either little further damping of the waves, or the waviness increased again. Ternovskaya and Belopolskii calculated that the optimum concentrations for wave damping corresponded to quantities of surfactant just sufficient to form a saturated monolayer at the interface (T10). 

The other two local equilibrium states (a2 and as) are coupled and gives sound wave propagation. When the sound wave damping is small compared to its rate of oscillation, the sound wave obeys a dispersion relation,... 

Fig. 36.—Changes in electromagnetic wave damping, A, as a function of starch humidity at various pressures. Three potato-starch varieties are denoted by three different point patterns. (Reprinted with permission from M. Boruch, S. Brzezinski, and A. Palka, Acta Aliment. Pol., 11 (1985) 115-124.)...

Sound waves—Damping—Congresses. I. Corsaro, Robert D. 

Clearly, type-I migration presents a problem for models of planet formation, both in terms of accreting fully formed planets before they migrate into the Sun and in terms of their survival once fully formed. However, it is likely that a sufficiently massive planet would have cleared a gap in the disk gas. Once this gap extended beyond the Lindblad resonances, type-I migration ceased. At present, there is considerable uncertainty about how massive a planet must be to clear a gap in the disk. This depends sensitively on the way in which waves damped in the nebula, and on the disk viscosity, both of which are poorly constrained. A recent estimate is that a body with a mass of 2-3M would have cleared a gap at 1 AU, while at 5 AU, a body 15M would do the job (Rafikov, 2002). 

Of the various other methods we mention a few of a more dynamic nature. From wave damping yiw) can in principle be obtained co is the frequency of the applied wave. See sec. 3.6g. Guido and Villone ) proposed a procedure to obtain interfacial tensions from the rate at which shear-deformed droplets retracted to their equilibrium spherical shape. De Hoog and Lekkerkerker ) determined very low interfacial tensions by following the initial state of the Rayleigh break-up of elongated drops. Although these methods are unlikely to develop into routine procedures, they demonstrate how wide the methodical spectrum is. 

In this section we address the measurement of interfacial tensions that are time dependent because the interface is not at equilibrium. Sometimes such tensions are called dynamic surface tensions but we prefer non-equilibrium surface tensions. Their measurement will be discussed in this section, particularly against the background of the techniques described so far. Most of the interpretation (in terms of surface rearrangements, transport to and from interfaces, etc.) and additional monolayer techniques (wave damping, for instance) will be deferred to chapters 3 and 4. 

After elimination of A and B between [3.6.61 and 62[ a determinant equation remains. It leads to two roots for the complex wave number fc, one corresponding to transverse and the other to longitudinal waves. With all of this completed, the mathematical framework for the analysis of wave damping is in principle available. Application to real systems is another matter. To illustrate this we shadl first consider some special cases and thereafter consider relaxation in Langmuir monolayers (sec. 3.6.8). It is recalled that A represents the linear part of the flow... 

Surface rheology Viscoelasticity of the monolayer differentiation between fluid and solid phases. Surface elasticity and viscosity in the transversal and longitudinal mode wave damping characteristics. Relaxation processes in monolayers. Mechanical stability of the monolayer. Interpretation often complicated because several molecular processes may be involved and because viscous and elastic components may both contribute. 

Grlgorev et al. found for C,2Pyridinium bromide monolayers an additional maximum in the wave damping which could be attributed to (de-)micellizationl). 

Knutson, P., Brochu, R., Seelig, W., and Inskeep, M. (1982) Wave damping in Spartina alterniflora marshes, Wetlands 2, 87-104. 

Hiihnerfuss, H Lange, P. A. Walter, W. (1985). Relaxation effects in monolayers and their contribution to water wave damping. I. J. Collord Interface Sci. 108, 430-441. 

The basis for our present models describing wave damping by monomolecu-lar surface films was formed by a paper published by Marangoni in 1872 ... 

A more precise interpretation of water wave damping through the elastic nature of a spread oil film was given by Reynolds (1880). The full text is as follows ... 

The first to perform wave-damping measurements in a kind of Langmuir trough, i.e., under different compression status of the monolayer, was Agnes Pockels (1891). Ironically, she described for the first time an apparatus that was... 

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