Capillary waves, generation

Zhang X (1995) Capillary-gravity and capillary waves generated in a wind wave tank Observations and theories. J Fluid Mech 289 51-82... 

Wind over waves coupling. J Geophys Res 104 7613-7623 Perlin M, Lin H, Ting CL (1993) On parasitic capillary waves generated by steep gravity waves an experimental investigation with spatial and temporal measurements. J Fluid Mech 255 597-620... 

This expression for capillary waves has been used as the basis for the measurement of surface tension by measuring the propagation velocity of capillary waves generated at a predetermined frequency (see Levich 1962 and, for a more recent approach using laser light scattering. Hard et al. 1976). 

We have reported [66] a limited study of spread polymethyl methacrylates and polyethylene oxide. Figure 12.19 shows the variation in surface tension, shear viscosity and dilational modulus obtained from SQELS data as a function of surface concentration. The viscoelastic moduli both show maximum values at finite values of the surface concentration. As the capillary waves generate oscillatory stress and strain, these are related via the complex dynamic modulus of the surface... 

Capillary waves may be generated mechanically by means of an oscillating bar, and for this case one writes the solutions to Eqs. IV-25 and IV-26 in the form... 

The capillary wave frequency is detected by an optical heterodyne technique. The laser beam, quasi-elastically scattered by the capillary wave at the liquid-liquid interface, is accompanied by a Doppler shift. The scattered beam is optically mixed with the diffracted beam from the diffraction grating to generate an optical beat in the mixed light. The beat frequency obtained here is the same as the Doppler shift, i.e., the capillary wave frequency. By selecting the order of the mixed diffracted beam, we can change the wavelength of the observed capillary wave according to Eq. (11). 

Ultrasonic atomization is sometimes also termed capillary-wave atomization. In its most common form, 142 a thin film of a molten metal is atomized by the vibrations of the surface on which it flows. Standing waves are induced in the thin film by an oscillator that vibrates vertically to the film surface at ultrasonic frequencies. The liquid metal film is broken up at the antinodes along the surface into fine droplets once the amplitude of the capillary wave exceeds a certain value. The most-frequent diameter of the droplets generated is approximately one fourth of the wavelength of the capillary wave,1 421 and thus decreases with increasing frequency. 

Analytical and empirical correlations for droplet sizes generated by ultrasonic atomization are listed in Table 4.14 for an overview. In these correlations, Dm is the median droplet diameter, X is the wavelength of capillary waves, co0 is the operating frequency, a is the amplitude, UL0 is the liquid velocity at the nozzle exit in USWA, /Jmax is the maximum sound pressure, and Us is the speed of sound in gas. Most of the analytical correlations are derived on the basis of the capillary wave theory. Experimental observations revealed that the mean droplet size generated from thin liquid films on... 

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...

Benjamin recently found for a 1,2-dichloroethane-water model system that, although the interface was molecularly sharp on time-average over hundreds of picoseconds, thermal fluctuations superimposed capillary waves as long as 0.8 nm on the sharp interface and generated a rough surface on the timescale of tens of... 

Fig. 1 illustrates the two mechanisms proposed for the processes of liquid disintegration and aerosol generation within ultrasonic nebulizers. The capillary-wave theory relates to the production of capillary waves in the bulk liquid. These waves constructively interfere to form peaks and a central geyser. When the amplitude of the applied energy is sufficiently high, the crests of the capillary waves break off, and droplets are formed. The rate of generation of capillary waves is dependent on both the physicochemical properties of the nebulized fluid and the intensity of the ultrasonic vibration. Mercer used Eq. (1) to calculate the threshold amplitude for the generation of capillary waves ... 

The second mechanism proposed for aerosol generation is based on the piezoelectric crystal operating at low frequency and imparting vibrations to the bulk liquid. This results in the formation of cavitation bubbles, which move to the air-liquid interface.The internal pressure within the bubbles equilibrates with that of the atmosphere, causing their implosion. When this occurs at the liquid surface, portions of the liquid break free from the turbulent bulk liquid, resulting in droplet formation. The dependence of atomization on cavitation phenomena has been demonstrated for frequencies between 0.5 and 2.0 MHz.Boguslavskii and Eknadiosyants combined these theories with-their proposal that droplet formation resulted from capillary waves initiated and driven by cavitation bubbles. 

Depth profiling techniques applied to thermodynamically equilibrated thin films characterize the compositions of coexisting phases and the spatial extent of the separating interface. This procedure repeated at different temperatures yields the coexistence curve and the corresponding temperature variation of the interfacial width. Determined coexistence curves are well described by the mean field theory with composition-dependent bulk interaction parameter [74]. The same interaction parameter also seems to generate the interfacial widths in accordance with results presented here [107] (Sect. 2.2.2) and elsewhere [88, 96, 129]. These predictions may however need to be aided by capillary wave contributions to fit another observations [95, 97, 98], especially those tracing the change of the interfacial width with film thickness [121,130] (see Sect. 3.2.2). 

Assume that a capillary wave of wavelength X is generated by a locahzed deformation ti (pulse) of the free surface of a liquid layer of thickness h. If h < X and q the wave propagation occurs with a linear phase velocity this is a result typical of waves in shallow waters. 

Measurements of surfactant concentrations on travelling capillary waves is complicated by the rapid decay rate of these waves, necessitating measurements close to the source of wave generation. To avoid this complication, we utilized a field of standing capillary waves. The wave tank was a circular (6.99 cm, inner diameter) glass vessel. The inner wall was coated with paraffin to avoid loss of the surfactant to the tank side walls. Triply distilled water was used as the substrate. The tank was overflowed to clean the surface prior to spreading the insoluble hemicyanine surfactant mono-layer at a surface concentration of 0.288 pg cm"2. Hemicyanine, 4-[4-(dimethylamino)styrl]-l-docosyl-pyridinium bromide, is a stilbazolium dye molecule to which is attached on one end a saturated twenty two car-... 

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