Standing waves, liquid surface

In a bath-type sonochemical reactor, a damped standing wave is formed as shown in Fig. 1.13 [1]. Without absorption of ultrasound, a pure standing wave is formed because the intensity of the reflected wave from the liquid surface is equivalent to that of the incident wave at any distance from the transducer. Thus the minimum acoustic-pressure amplitude is completely zero at each pressure node where the incident and reflected waves are exactly cancelled each other. In actual experiments, however, there is absorption of ultrasound especially due to cavitation bubbles. As a result, there appears a traveling wave component because the intensity of the incident wave is higher than that of the reflected wave. Thus, the local minimum value of acoustic pressure amplitude is non-zero as seen in Fig. 1.13. It should be noted that the acoustic-pressure amplitude at the liquid surface (gas-liquid interface) is always zero. In Fig. 1.13, there is the liquid surface... 

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. 

Mineral-liquid or mineral-gas interfaces under reactive conditions cannot be studied easily using standard UHV surface science methods. To overcome the pressure gap between ex situ UHV measurements and the in situ reactivity of surfaces under atmospheric pressure or in contact with a liquid, new approaches are required, some of which have only been introduced in the last 20 years, including scanning tunneling microscopy [28,29], atomic force microscopy [30,31], non-linear optical methods [32,33], synchrotron-based surface scattering [34—38], synchrotron-based X-ray absorption fine structure spectroscopy [39,40], X-ray standing wave... 

Another interesting effect that plays a role in the design of the proper housing for QCM in liquid is the generation of compressional standing waves. This can be observed when the crystal oscillates in parallel with a vessel wall in close proximity, which acts as a reflector (Fig. 4.10 Janshoff et al., 2000 Schneider and Martin, 1995). The effect can be observed over the distance of the reflector surface (e.g., 100pm Lin and Ward, 1995 Schneider and Martin, 1995). 

Bedzyk MJ (1992) X-ray standing wave studies of the liquid/solid interface and ultrathin organic films. In Springer Proceedings in Physics. Vol 61 Surface X-ray and Neutron Scattering. Zabel H, Robinson IK (eds) Springer-Verlag, Berlin, p 113-117... 

The earliest known formula for the standing wave ultrasonic nozzle was derived by Mochida [93]. He found that the SMD of a nozzle was a function of the volumetric flow rate, liquid density, viscosity, and surface tension. His results were confined to only a single frequency of 26 kHz. A limitation on the volumetric flow rate also exists of up to 50 L/h, and there is a limitation of the liquids that may be used. 

In contrast, the disturbance caused by the ultrasound oscillator induces characteristic oscillations within the given liquid column, corresponding to its geometry and its physical characteristics. Expression defining a number of possible values of the liquid column oscillation frequencies is obtained as a solution of the corresponding rate potential function for the standing wave formed on the meniscus surface, in the form [1-2] ... 

The liquid contained in an upright cylinder subjected to horizontal seismic excitation X t) may be considered as ideal fluid (potential flow) resulting in a hydrodynamic problem (Ibrahim 2005) associated with the motion of the liquid free surface and the development of standing waves. The solution of the hydrodynamic problem shows that the liquid motion can be expressed as the sum of two separate contributions, called impulsive and convective, respectively. The impulsive component of the motion satisfies exactly the boundary conditions at the tank wall and the bottom of the tank and corresponds to zero pressure at the free surface of the fluid. It represents the motion of the fluid part that follows the motion of the container. The convective term is associated with liquid sloshing of... 

As the interfacial velocity, Ui, between the gas and the liquid increases, the break up process changes, because this velocity reinforces standing surface waves, which leads to a more complex jet break up, which occurs as a result of transverse oscillations. When the interfadal velocity, Uj, is higher still, the droplets shatter into very fine droplets. The most important droplet stability criteria is the ratio of aerodynamic forces to surface tension forces defined by the Weber number [7, pp. 18—60], D we ... 

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