Quantify dependent-scattering effects in dense gas–solid suspensions

Quantify the dependent-scattering effects arising from near-field electromagnetic coupling between particles in the denser regions of gas–solid flows, where the mean inter-particle separation is comparable to or smaller than the terahertz wavelength, and determine their impact on solids-concentration retrieval using the independent-particle Mie-scattering closure.

Background

The inversion framework models the particulate medium using an independent-scattering closure in which each particle is treated as an isolated Mie scatterer and the volumetric backscatter and extinction coefficients are obtained by multiplying single-particle cross-sections by the particle number density. The authors assess the validity of this approximation using the mean inter-particle separation relative to the wavelength.

Although the retrieved profiles are broadly consistent with pressure-derived concentration estimates, the mean separation-to-wavelength ratio becomes much smaller than unity in the densest lower-riser regions. Near-field coupling between particles may therefore alter the scattering response, but the present model does not represent that effect. Determining whether and how dependent scattering changes the inversion is consequently an unresolved problem, particularly for denser or more strongly attenuating industrial flows.

References

Dependent (near-field) coupling between scatterers is a separate limitation: evaluating \cref{eq:mean_distance} across the profiles, the mean inter-particle separation relative to the wavelength ranges from $\langle d\rangle/\lambda\approx5\times10{-2}$ in the densest range bins to $\sim!2.5$ near the riser roof. Dependent-scattering effects therefore cannot be excluded where $\langle d\rangle\lesssim\lambda$; this limitation is most pronounced in the denser lower riser and relaxes progressively toward the dilute upper region, and it is not represented by the independent-particle closure.

— Terahertz Radar Inversion for Range-Resolved Solids Concentration Profiling in Gas--Solid Flows  (2609.18567 - Jepsen et al., 16 Sep 2026) in Section Measurement Results and Discussion, paragraph beginning “The independent-scattering closure…”