Collective versus individual dispersion dynamics: vortex-ring modification across suspensions and polymer solutions

We show that vortex rings forming in suspensions and polymer solutions exhibit similar behaviour in terms of vortex-core growth, vorticity redistribution and circulation when compared at loadings (i.e. volume fraction in suspensions and concentration in polymer solutions) normalised by their respective critical loading. This suggests that the collective, loading-driven dynamics of dispersed particles or polymer chains can outweigh the unique characteristics of the dispersion and govern certain aspects of the flow response. Using a confined vortex ring as a canonical structure, we synthesise experimental data spanning dilute to concentrated regimes for both media, with our analysis indicating that similar collective dynamics exist in both systems. Specifically, the vortex-core growth rate relative to the unloaded case increases approximately linearly with normalised loading while circulation remains nearly unchanged over the measured parameter range. Shared collective dynamics are further suggested by radial vorticity profiles scaled according to loading, which reveal structural markers that align along consistent non-dimensional radii, demonstrating a topological self-similarity between flow fields despite fundamentally different disperse phases. Turbulent kinetic energy trends expose the limits of this correspondence: with increasing Reynolds number, turbulence rises in suspensions but remains largely unchanged in polymer solutions, reflecting differences in how semi-rigid particles and flexible chains interact with small-scale fluctuations. Altogether, these results uncover shared collective dynamics and support the cautious use of polymer analogues to study suspension flows within an equivalent loading regime. However, the limited test matrix motivates further experiments involving different flow media to assess the generality of these findings.