Spheroidal probability distribution

An approach somewhat similar to that in Section 8.5 was taken by O Neill and Ignatiev (1978), who obtained an expression for the average dielectric function of a mixture containing spheroidal inclusions with ratios of semi-minor to semimajor axes given by a probability distribution function. 

In terms of spheroidal coordinates, the probability distribution as obtained directly from Equation (13) is separable,... 

Figure 4. Polar plots of angular probability distributions for the spheroidal hybrids up through n = 4, for ZR = 0 (solid line), 15 (.. . . ), and oo(dashed line). The z-axis is horizontal.

In colloidal suspensions, the sound propagation is typically governed by the acoustophoretic motion of particles. For monodisperse spheroids that do not deviate too much from spherical shape (aspect ratio <10/1), the attenuation spectrum essentially reflects the volume specific surface area of the particles (Babick and Richter 2006). Similar results would probably be obtained for any convex particle shape. For particle aggregates, the inner structure is decisive. Regarding the type of quantity, acoustically measured size distributions are ideally volume weighted distributions (see comments in Sect. 2.2). 

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