Capillary ripples

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... 

Erik s research focused on the interfacial properties of the ocean surface, and, in particular, how the chemistry of the air-sea interface affects the dynamics of short waves, nearsurface flows and interfacial fluxes of heat, mass and momentum. During his short career, he contributed to over 30 scientific publications in this area. His doctoral research, carried out under the tutelage of well-known colloid and surface chemist, Sydney Ross, concerned the propagating characteristics of surface waves in the presence of adsorbed films. That work was eventually published as a series of seminal papers on capillary ripples, and his theoretical treatment of ripple propagation and a corrected dispersion relation for surface waves in the presence of a surface dilational modulus (with J. Adin Mann, Jr.) still stand as the definitive word on the subject. 

Mann JA, Hansen RS (1963) Propagation characteristics of capillary ripples. II. Instrumentation for measurement of ripple velocity and amplitude. J Colloid Sci 18 757-771... 

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. 

In an acoustic atomizer, high-frequency sound waves are used to create capillary ripples that ultimately break up into droplets. Ultrasonic atomization can produce a fairly narrow droplet size distribution. 

The interfacial tension, y, in the Gibbs adsorption equation is used for equilibrium conditions as bitumen components are adsorbed. Measurement techniques available are extensive. Some of these methods are duNouy ring, maximum bubble pressure, drop volume, Wilmhelmy plate, sessile drop, spinning drop, pendant drop, capillary rise, oscillating jet, and capillary ripples. These and many others are referenced extensively by Malhotra and Wasan (153). These authors also showed that there is no correlation between emulsion stability and interfacial tension. The nature of the film dominates stability. Some relationships between interfacial tensions and crude oil properties follow. 

Recently, Hanratty presented a comprehensive review of the attempts to account for the interfacial waviness in modelling the interfacial shear stress for the stability analysis of gas-liquid two-phase flows [53]. Basically, the approach taken was to implement the models obtained for the surface stresses in air flow over a solid wavy boundary as a boundary condition for the momentum equation of the liquid layer over its it mobile wavy interface. Craik [98] adopted the interfacial stresses components which evolve from the quasi-laminar model by Benjamin [84]. Jurman and McCready [99], Jurman et al. [100], and Asali and Hanratty [101] used correlated experimental values of shear stress components (phase and amplitude) based on turbulent models which consider relaxation effects in the Van Driest mixing length. Since the characteristics of the predicted surface stresses are dependent on the wave number, Asali and Hanratty picked the phase and amplitude values which correspond to the wave lengths of the capillary ripples observed in their experiments of thin liquid layers sheared by high gas velocities [101]. It was shown that the growth of these ripples is controlled by the interfacial shear stress component in phase with the wave slope. 

The latter relation is known as Kelvin s equation. Methods for creating propagating capillary ripples typically involve either a mechanical or electrocapillary disturbance of the fluid interface [189-191]. The laser is more appropriate because it does not necessitate physical contact with the fluid surface [497]. The wave characteristics, which are necessary for the evaluation of the interfacial properties through the dispersion relation, are often determined by the reflection of a laser beam from the fluid surface to a position-sensitive photodiode. 

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