Capillary waves damping

Noskov BA (1998) Dynamic properties of heterogeneous surface films Multiple scattering of capillary waves. J Chem Phys 108 807-815 Wang Q, Feder A and Mazur E (1994) Capillary Wave Damping in Heterogeneous Monolayers. J Phys Chem 98 1272-1276 Waterman PC and Truell R (1961) Multiple scattering of waves. J Math Phys 2 512-537... 

Garrett, W.D. and Bultman, J.D., 1963. Capillary-wave damping by insoluble organic monolayers. J. Colloid Sci., 18 798—801. 

The modern resurgence in interest in capillary wave hydrodynamics, which started in the early 1950s, centers around the damping effects and the presence of a viscoelastic film between two fluids [37,49-56]. All are more or less similar, in the assumptions invoked and the hydrodynamic theory used. The Lucassen-Reynders-Lucassen [55] and Kramer s [56] dispersion equations are essentially identical except Kramer ignores the gravity wave at the outset which is consistent with the wave vector range often used experimentally, and this is seen in Fig. 3. 

Fig. 4 General solution for the dispersion equation on water at 25 °C. The damping coefficient a vs. the real capillary wave frequency o> , for isopleths of constant dynamic dilation elasticity ed (solid radial curves), and dilational viscosity k (dashed circular curves). The plot was generated for a reference subphase at k = 32431 m 1, ad = 71.97 mN m-1, /i = 0mNsm 1, p = 997.0kgm 3, jj = 0.894mPas and g = 9.80ms 2. The limits correspond to I = Pure Liquid Limit, II = Maximum Velocity Limit for a Purely Elastic Surface Film, III = Maximum Damping Coefficient for the same, IV = Minimum Velocity Limit, V = Surface Film with an Infinite Lateral Modulus and VI = Maximum Damping Coefficient for a Perfectly Viscous Surface Film...

Fig. 6 The effect of transverse viscosity on the polar plot of Fig. 4. The damping coefficient, a, is plotted vs. the real capillary wave frequency, 0> for several different transverse viscosities (/x in the figure has units of 10 5 mNsm ). Only the isopleths for Sd = 0 and k = 0 are shown to give the outermost loop of Fig. 4. The plot was generated using the same condition as in Fig. 4, k = 32 431 m, ad = 71.97mN nr1, p = 997.0 kg nr3, r) = 0.894 mPa s and g = 9.80 m s 2...

The experimental methods for the determination of liquid viscosity are similar to those used for gases ( 8.VII F) (i) transpiration, through capillaries, (ii) torque on rotating cylinders, or the damping of oscillating solid discs or spheres, in the liquid, (iii) fall of solid spheres through the liquid, (iv) flow of liquid through an aperture in a plate, (v) capillary waves. Methods (i) and (ii) are mostly used for absolute, the others for comparative, measurements. 

Henceforth we shall use the term capillary waves, or capillary ripples for waves that are so small that interfacial tension contributes significantly to their properties. Two types of such waves can be distinguished spontaneous, or thermal waves and those externally applied. The former type is always present they are caused by spontaneous fluctuations cind have a stochastic nature. In secs. 1.10 and 1.15 it was shown how from these fluctuations interfacial tensions and bending moduli could be obtained. Now the second type will be considered. Transverse or longitudinal perturbations can be applied to the interface, for example by bringing in a mechanically driven oscillator (see sec. 3.7). Such waves are damped, meaning that the amplitude Is attenuated. Damping takes place by viscous friction in the... 

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