Longitudinal waves damping

Recently, reliable relaxation experiments at liquid/liquid have been performed by different techniques. Bonfillon Langevin (1993) measured the dilational elasticity of different surfactants (Triton X-100, SDS in water and in 0.1 M NaCl) at water/air as well as alkane/water interfaces by a modified longitudinal wave damping method (cf. Section 6.3.1). While at the water/air interface, the behaviour of Triton X-100 could be described by a... 

Dilational elasticity modulus of Triton X-lOO solutions at the water/dodecane interface determined from longitudinal wave damping according to Bonfillon Langevin (1993)... 

Graham Phillips (1980a) measured the dilational elasticity of BSA and lysozyme by longitudinal wave damping (2 to 10 cpm). The elasticity values calculated from tt-A isotherms... 

Fig. 6.17 Dilational elasticity modulus determined from longitudinal wave damping experiments,BSA(B), lysozyme(D) according to Graham Phillips (19S0a)...

There are various direct measurements of micellar solutions giving access to the dynamics rate constants - mainly based on disturbance of the equilibrium state by imposing various types of perturbations, such as stop flow, ultrasound, temperature and pressure jump [14,15[. This aspect is also not further elaborated here we focus instead on the impact of micellar kinetics on interfacial properties, to demonstrate that tensiometry and dilational rheology are suitable methods to probe the impact of micellar dynamics. The first work on this subject was published by Lucassen already in 1975 [16[ and he showed that the presence of micelles in the bulk have a measurable impact on the adsorption kinetics, and hence on the dilational elasticity, when measured by a longitudinal wave damping technique. Subsequent work demonstrated the effect of micellar dynamics on non-equilibrium interfacial properties [17-29]. The physical idea of the impact of micellar dynamics on the dynamic properties of interfacial layers can be easily understood from the scheme given in Figure 13.1. 

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... 

From the dispersion equations Lucassen and van den Tempel l derived the following relation between K° and the (distance) damping coefficient p for longitudinal waves... 

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. 

One of the most remarkable and most frequently studied effects of surface rheology is the damping of surface waves. Surface waves, transversal and longitudinal waves, are described by dispersion equations. Maim (1984) gave recently an overview on modem aspects of dynamic surface tension and capillary waves. 

In the present chapter current relaxation theories will be described first both damping of harmonically generated disturbances and relaxations to transient perturbations. Thereafter, experiments are described, based on the damping of capillary and longitudinal waves, oscillation behaviour of bubbles. Also transient relaxations with pendent drop and drop and bubble pressure measurements are shown. Finally, applications to different interfaces, using surfactants, surfactant mixtures, polymers and polymer/surfactant mixtures are discussed. 

To perform measurements of longitudinal wave propagation and damping characteristics, a device designed by Lemaire Langevin (1992) can be used. While the longitudinal wave is... 

Serrien et al. (1992) measured the damping of planar longitudinal waves, generated with a barrier on a Langmuir trough and detected with a Wilhelmy balance. The longitudinal waves correspond to slow periodic compressions/dilations of the protein adsorption layer (BSA, casein). The results for BSA are shown in Fig. 6.18. Further experiments using a stress... 

To calculate the sound velocity and damping, the simple model (51), (52) is not sufficient. Since sound is a longitudinal wave of the mass density, both the longitudinal component of the velocity, Vl(t, t), and the pressure field p(r, t) have to be taken into account in this case in addition to (r, t) and Vr(r, t) [132,135,136]. The frequency-dependent sound velocity c (cu) and damping >(cu) can then be obtained from the pole structure of the pressure correlation function in the hydrodynamic limit 0, where... 

A longitudinal wave propagation approach has been adopted in view of the problems of applying capillary wave techniques to liquid/liquid interfaces. These arise from two quarters. Firstly the variation of damping coefficient with elastic modulus can be shown (12) to be negligible at sufficiently high and low elastic moduli. 

Y. Goda, Wave damping characteristics of longitudinal reef system. Advances in Coastal Structures and Breakwaters 95, London (1995) M. D. Groenewoud, J. van de Graaff, E. W. M. Claessen and S. C. van der Biezen (eds.). Effect of submerged breakwater on profile development, 25th ICCE, Orlando, USA (1996). 

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