Random wobbling

Large drops (De =1 cm) of chlorobenzene will fall through water with a somewhat erratic oscillatory motion (L3). The drop pitches and rolls. The flight is not vertical but is erratically helical in nature. A series of oscillations, accompanied by waves moving over the interface, can cause the drop to drift several inches in a horizontal direction in a range of a foot or two of fall. Such drops can not oscillate violently as described above, due to the damping action of such movement by the sliding side-wise motion of the wobble. Motion pictures indicate that internal circulation is also considerably damped out by this type of oscillation. Rate of 

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Moreover, ellipsoidal bubbles and drops commonly undergo periodic dilations or random wobbling motions which make characterization of shape particularly difficult. Chapter 7 is devoted to this regime. 

In general, oscillations may be oblate-prolate (H8, S5), oblate-spherical, or oblate-less oblate (E2, FI, H8, R3, R4, S5). Correlations of the amplitude of fluctuation have been given (R3, S5), but these are at best approximate since the amplitude varies erratically as noted above. For low M systems, secondary motion may become marked, leading to what has been described as random wobbling (E2, S4, Wl). There appears to have been little systematic work on oscillations of liquid drops in gases. Such oscillations have been observed (FI, M4) and undoubtedly influence drag as noted earlier in this chapter. Measurements (Y3) for 3-6 mm water drops in air show that the amplitude of oscillation increases with while the frequency is initially close to the Lamb value (Eq. 7-30) but decays with distance of fall. 

There is some evidence that isolated drops may shake themselves apart if shape oscillations become sufficiently violent (L7). It has been suggested (El, Gil, H22) that breakup occurs when the exciting frequency of eddy shedding matches the natural frequency of the drop. However, other workers (S7) have found that oscillations give way to random wobbling before breakup occurs. While it is possible that resonance may produce breakup in isolated cases, this mechanism appears to be less important than the Taylor instability mechanism described above. 

The virtual volume coefficient Cy for potential flow around a sphere is 0.5. For ellipsoidal bubbles with a ratio of semiaxes 1 2, Cy is 1.12. For ellipsoidal bubbles with random wobbling motions, Fopez de Bertodano [26] calculated to be about 2.0. In addition, Cy is a function of the specific gas holdup [27-29] ... 

Particles subject to Brownian motion tend to adopt random orientations, and hence do not follow these rules. A particle without these symmetry properties may follow a spiral trajectory, and may also rotate or wobble. In general, the drag and torque on an arbitrary particle translating and rotating in an unbounded quiescent fluid are determined by three second-order tensors which depend on the shape of the body ... 

This effect may be explained in terms of the quantum theory of electrodynamics. According to this theory each mode of the quantized radiation field possesses a zero-point energy of hu)/2. This implies that, even in the absence of external radiation, the mean square value of the time-depen-dent electric field is finite and that a hydrogen atom will experience a perturbation produced by the fluctuations in this field. These zero-point fluctuations cause the electron to wobble randomly in its orbit and so smear the charge over a greater volume of space. Since the electron is bound to the nucleus by a non-uniform electric field, the reduction in electron density causes a shift in the atomic energy levels. This Lamb shift, as it is now called, is greatest for those states in which iK0) is finite, i.e. the n states. 

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