Low-frequency scattering by correlated distributions of randomly oriented particles

Abstract

Random distributions of correlated scatterers averaged over orientation are considered, corresponding to isotropic fluids of statistical mechanics particles (with volume v, number concentration ρ, and volume fraction w=ρv). For minimum separation of centers small compared to wavelength and acoustic particle parameters close to the embedding medium’s, the incoherent differential scattering from unit volume and the corresponding attenuation coefficient are proportional to the fluctuations (variance) in number concentration. For arbitrary convex hard particles (e.g., ovals or simple polyhedra, repulsive at contact) with shape parameter c≥3, the variance is expressed in terms of a quotient S(c;w) of polynomials in w that has a maximum S■(c) at w■(c). Spheres (c=3) were considered earlier. For c>3, the fluctuations and S■ and w■ are smaller than for spheres; for c<3 (which we consider formally), they are larger than for spheres. The results are interpreted by comparing leading terms with the second virial coefficients for more general statistical mechanics models. Scattering data for suspensions of discoidal red blood cells versus w under different flow conditions can be fitted adequately by S(c;w) for different values of c<3. The low values of c suggest weaker repulsion between deformable cells, and attractive interparticle forces mediated by flow and aggregative trends.