Flow-induced aggregation of colloidal particles leads to aggregates with fairly high fractal dimension $\left(d_f\simeq 2.4–3.0\right)$ which are directly responsible for the observed rheological properties of sheared dispersions. We address the problem of the decrease in aggregate size with increasing hydrodynamic stress, as a consequence of breakup, by means of a fracture-mechanics model complemented by experiments in a multipass extensional (laminar) flow device. Evidence is shown that as long as the inner density decay with linear size within the aggregate (due to fractality) is not negligible (as for $d_f\simeq 2.4–2.8$), this imposes a substantial limitation to the hydrodynamic fragmentation process as compared with nonfractal aggregates (where the critical stress is practically size independent). This is due to the fact that breaking up a fractal object leads to denser fractals which better withstand stress. In turbulent flows, accounting for intermittency introduces just a small deviation with respect to the laminar case, while the model predictions are equally in good agreement with experiments from the literature. Our findings are summarized in a diagram for the breakup exponent (governing the size versus stress scaling) as a function of fractal dimension.

• Received 23 January 2009

DOI:https://doi.org/10.1103/PhysRevE.79.061401