  Flow-induced aggregation of colloidal particles leads to aggregates with
fairly high fractal dimension () which are directly responsible for the
observed rheological properties of sheared dispersions. We address the problem
of the decrease of aggregate size with increasing hydrodynamic stress, as a
consequence of breakup, by means of a fracture-mechanics model complemented by
experiments in a multi-pass 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), this imposes a
substantial limitation to the hydrodynamic fragmentation process as compared
with non-fractal 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.
