Three length-scales colloidal gels: The clusters of clusters versus the interpenetrating clusters approach

Typically, in quiescent conditions, attractive colloids at low volume fractions form fractal gels structured into two length scales: the colloidal and cluster scales. However, when flow interferes with gelation gels, it may display three distinct scales [Dagès et al., Soft Matter 18, 6645–6659 (2022)]. Following those recent experimental investigations, we derive models that account for structure rheological properties of such atypical gels. The gel elasticity is inferred from scaling arguments, translated scattering intensities following global functions approach proposed by Beaucage and, typically, measured small-angle x-ray (SAXS). In both models, consider condensate clusters. clusters model, superagregates then build network. interpenetrating interpenetrate one another to Those are used analyze rheo-SAXS experiments carried out on carbon black formed through cessation.