Standing-wave field

Figure Cl.4.3. Schematic diagram of the Tin-periD-lin configuration showing spatial dependence of the polarization in the standing-wave field (after 1171).

The coalescence of bubbles is driven by the two mechanisms. One is the attractive radiation force between bubbles called secondary Bjerknes force. The other is the other radiation force called the primary Bjerknes force which drives active bubbles to the pressure antinode of a standing wave field, ft should be noted, however, too strong acoustic wave repels bubbles from the pressure antinode as described in the next section [29, 30]. 

Fig. 13.12 Photographs of sonoluminescence from sulfuric acid solution of Na2SC>4, illustrating the spatial separation of sodium (orange) and continuum (blue-white) emissions using a horn-type transducer at 20 kHz (a) [38] (Reprinted from American Chemical Society. With permission) and using standing-wave fields at 28 kHz in a cylindrical beaker (b) [39]...

Figure 31. Depiction of the X-ray standing wave field formed by the interference between incident and Bragg reflected beams.

Spengler, J. F. Jekel, M. Christensen, K. T. Adrian, R. J. Hawkes, J. J. Coakley, W. T., Observation of yeast cell movement and aggregation in a small scale MHz ultrasonic standing wave field, Bioseparation 2000, 9, 329 341... 

Istead of using the single-field Eq. (12.58), we pass the molecules in this super-isition state through a bichromatic standing-wave field of the form ... 

By numerical integration of the Bloch equations describing the classical trajectory of an atom from the nozzle through the standing wave field at 243 nm to the detector and integration over all possible trajectories and over the velocity distribution of the atoms, a theoretical line shape is deduced which is then fitted to the experimental data. The solid lines in Fig. 2 are obtained from this fitting procedure. 

The capabilities of ultrasonic radiation forces for manipulating suspended particles have been the subject of a broad spectrum of experimental research. The effectiveness of particle-liquid separation by ultrasonic radiation forces depends on the acoustic distribution in a standing-wave field. In a US standing wave, suspended particles of appropriate... 

The axial component of the primary acoustic radiation forces, which is parallel to the z-direction of the ooordinates and accelerates the particles towards the pressure nodal planes of the standing wave field. 

Yasuda and Kamakura [3] and Mandralis and coworkers [4] have demonstrated that it is possible to generate standing-wave fields between a transducer and a reflecting wall, although of much larger dimensions (1-20 cm) than across a FFF channel. Sound travels at a velocity of 1500 m/s through water, which translates to a wave of frequency of approximately 6 MHz for a 120-pm thick FFF channel. 

It is interesting to observe that response differences between the coatings decrease when the frequency is increased. This is probably connected with the respective values of the wavelength and of the thickness of the layer in which absorption takes place which was estimated to be around 120 pm thick. The influence of the relative size of the probe compared to the wavelength was studied in standing waves fields [33]. As expected, maxima and minima were observed for the probe response. The ratio of the temperature rise at pressure maxima and minima... 

The x-ray standing-wave technique represents an extremely sensitive tool for determining the position of impurity atoms within a crystal or adsorbed onto crystal surfaces. This technique is based on the x-ray standing-wave fields that arise as a result of the interference between the coherently related incident and Bragg-diffracted beams from a perfect crystal, and is described by the theory of dynamical diffraction of x-rays. ... 

Figure 24. (A) Depiction of specular and first-order Bragg reflection from a surface. (B) Generation of an x-ray standing-wave field. (C) Movement of an x-ray standing-wave field in the — H direction upon advancing the angle of incidence across a Bragg reflection. (From Abruna, H. D., White J. H., et al., J. Phys. Chem. 92, 7045 (1988), with permission.)...

The electric field intensity of the standing-wave field at a point r is given by... 

Particle separation methods based on the effects on suspended particles of exposure to an ultrasonic standing-wave field have been reported [51]. Carrier medium exchange in a laminar flow microchannel has also been achieved using... 

Figure 1. Top A standing wave field formed from the superposition of two traveling plane waves of wavelength X and intersection angle (scattering angle) 26. The standing wave period is D as defined in Equation (1). Bottom The two traveling planes waves are represented in reciprocal space by wave vectors K0 and KR. K0 = KR= . The standing wave is defined by standing-wave vector Q defined in Equation (2).

Figure 2. X-ray standing wave field formed in a crystal and above its surface by the interference of incident and Bragg-diffracted monochromatic X-ray plane waves. The inset shows the reciprocal space diagram for the Laue condition described by Equation (4).

From dynamical diffraction theory, the relative phase, v, of the standing wave field decreases by n radians as the incident angle is scanned from the low-angle side to the high-angle side of the rocking curve (i. e., from rf = 1 to ( = -1). According to Equation... 

Fischer CJ, Ithin R, Jones RG, Jackson GJ, Woodruff DP, Cowie BCC (1998) Non-dipolar photoemission effects in X-ray standing wave field determination of surface structure. J Phys Cond Matter 10 L623-L633... 

This fixes a maximum ai of 0.6 x 10 Hz. Our experimental work is actually generally limited to frequency offsets av < 0.3 x 10 Hz, and this will always be the case in experiments discussed in this paper. Over most of the central region of the cavity, then, excluding the nodal surfaces of the standing wave field, one may invoke the condition (aw =... 

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