Interfacial wave motion

Linde, H. et al.. Interfacial wave motions due to Marangoni instability. I. Traveling periodic wave trains in square and annular containers, J. Colloid Interface Sci., 188, 16-26, 1997. 

Capillary Ripples Surface or interfacial waves caused by perturbations of an interface. When the perturbations are caused by mechanical means (e.g., barrier motion), the transverse waves are known as capillary ripples or Laplace waves, and the longitudinal waves are known as Marangoni waves. The characteristics of these waves depend on the surface tension and the surface elasticity. This property forms the basis for the capillary wave method of determining surface or interfacial tension. 

When the 6 value was higher than 0c. the incident pulse was totally reflected at the interface between the PS and S-LAH79 substrate. That is, the NBD dye molecules near the interface were selectively excited by the evanescent wave. Hence, the data set obtained at 0 = 53.6° reflects the interfacial molecular motion. The inflection temperature, which can be assigned to the interfacial Tg (7 ) at 0 = 53.6°, was 386 K, and was discemibly higher than the T. This is direct evidence for depressed mobility at the interface. 

Chapter 5 considers the stabiUty of fluid interfaces, a subject pertinent both to the formation of emulsions and aerosols and to thdr destruction by coalescence of drops. The closely related topic of wave motion is also diseussed, along with its implications for mass transfer. In both cases, boundary eonditions applicable at an interface are derived—a significant matter because it is through boundary conditions that interfacial phenomena influence solutions to the governing equations of flow and transport in fluid systems. 

In the remainder of this book, we present information on phenomena where dynamic interfacial effects are important. We begin in this chapter with interfacial stability and the closely related subject of interfacial oscillation or wave motion. It is frequently of great interest to know the conditions for interfacial instability. We may ask, for instance, how far a fluid jet leaving a circular orifice travels before it breaks up into drops. Or when we can expect spontaneous convection to arise near an interface across which one or more species diffuse. 

We consider the simplest case of an insoluble surfactant. In the initial motionless state with a flat interface, the surfactant is uniformly distributed and interfacial tension is uniform. During wave motion, the local concentration of surfactant varies with position along the interface, with the result that interfacial tension gradients arise. Because these gradients influence the interfacial momentum... 

The above discussion has centered on wave motion imposed on a surface by, for instance, an oscillating bar. But thermal fluctuations cause wave motion of small amplitude even on interfaces that are not disturbed by external means. With laser light scattering techniques it is possible to measure interfadal tension from analysis of surface fluctuations. This method has been applied to the measurement of ultralow interfacial traisions between liquid phases (Bouchiat and Meunier, 1972 Cazabat et al., 1983 Zollweg et al., 1972). Presumably it could also be used to determine surface compressibility or other rheological properties. 

General Reeerences on Interfacial Stability and Wave Motion... 

The ratio of the imaginary part of to P is often called snrface viscosity, although in this case the complex natnre of E arises naturally from the diffusion problem and is umelated to any relationship between interfacial stress and the rate of strain. The reason for this terminology is that the analysis of wave motion in Chapter 5 is carried out without any explicit consideration of snrfactants, but... 

Velarde, M. G., Nepomnyashchy, A. A., and Hennenberg, M. (2000) Onset of oscillatory interfacial instability and wave motions in Benard layers. Adv. Appl. Mech. 37 167-237. 

A surfactant monolayer (or thin layer of oil) spread at a fluid interface damps the surface waves. This phenomenon is due to the fact that as the surfactant monolayer is compressed and expanded during the wave motion, the oscillations of the local surfactant concentration result in oscillations of the local interfacial tension. As a result, a combination of Marangoni and interfacial viscosity effects damp the surface waves. Following the classical approach of small-amplitude waves, Hansen and Ahmad [495] and Hedge and Slattery [496] derived the dispersion relation between the wave number k and wave frequency o) (see also Ref. 58) ... 

The longitudinal-wave method was first described by Lucassen [498]. Since Lucassen s original work, propagation characteristics of longitudinal waves have been widely used for measuring dilatational elasticity and interfacial viscosity of adsorbed surfactant monolayers. The pure longitudinal waves motion obeys the dispersion relation... 

Due to lack of understanding of the wave structure and motions, modeling of the interfacial shear remains empirical. 

Figure 3.42. Sketch of the interfacial motions occurring in monolayers, caused by propagating transversal (a) and longitudinal (b) waves. (Redrawn from M. van den Tempel, Chem. Ing, Techn. 23 (1971) 1260.)...

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