Rippled sphere

Volume-normalized extinction is plotted in Fig. 11.2 as a function of photon energy for several polydispersions of MgO spheres both scales are logarithmic. For comparison of bulk and small-particle properties the bulk absorption coefficient a = Airk/X is included. Some single-particle features, such as ripple structure, are effaced by the distribution of radii. The information contained in these curves is not assimilated at a glance they require careful study. 

The calculated extinction spectrum of a polydispersion of small aluminum spheres (mean radius 0.01 jam, fractional standard deviation 0.15) is shown in Fig. 11.4 both scales are logarithmic. In some ways spectral extinction by metallic particles is less interesting than that by insulating particles, such as those discussed in the preceding two sections. The free-electron contribution to absorption in metals, which dominates other absorption bands, extends from radio to far-ultraviolet frequencies. Hence, extinction features in the transparent region of insulating particles, such as ripple and interference structure, are suppressed in metallic particles because of their inherent opacity. But extinction by metallic particles is not without its interesting aspects. 

We discussed in Section 4.3 the electromagnetic normal modes, or virtual modes, of a sphere, which are resonant when the denominators of the scattering coefficients an and bn are minima (strictly speaking, when they vanish, but they only do so for complex frequencies or, equivalently, complex size parameters). But ext is an infinite series in an and bn, so ripple structure in extinction must be associated with these modes. The coefficient cn (dn) of the internal field has the same denominator as bn(an). Therefore, the energy density, and hence energy absorption, inside the sphere peaks at each resonance there is ripple structure in absorption as well as scattering. 

A glance at the curves in Fig. 11.15 reveals extinction characteristics similar to those for spheres at small size parameters there is a Rayleigh-like increase of Q a with x followed by an approximately linear region broad-scale interference structure is evident as is finer ripple structure, particularly in the curves for the oblate spheroids. The interference structure can be explained... 

Mie theory does an admirable job of predicting extinction by spherical particles with known optical constants even the finest details it predicts—ripple structure—have been observed in extinction by single spheres. Several different causes—a distribution of sizes or shapes, and absorption—have the same effect of effacing the ripple structure or even the broader interference structure. 

Asymptotic expressions for extinction and absorption efficiencies of spheres averaged over a size parameter interval Ax it (i.e., with no ripple structure) have been derived by Nussenzveig and Wiscombe (1980). 

Malyusov ei al. (M6), 1955 in very short wetted-wall columns (no rippling) (3) flowing over spheres. Entry and end effects studied, also effects of adding surfactant. Study of distillation in wetted-wall columns, taking into account the effects of laminar and turbulent flow of vapor phase. 

Deals with smooth and rippling flow of a liquid over a sphere or series of spheres, especially with the problem of mixing in the liquid film at the junctions of spheres. 

FIGURE 14.7 Schematic diagram of the envelopes of the Mie scattering curves for homogeneous, dielectric spheres (i.e., ignoring the ripple structure). Dashed lines are for the RDG limit at p = 0 with slope -4 and the p —>oo limit with slope -2. Solid line is the envelope for an arbitrary phase shift parameter p. 

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