  By characterising the hydrodynamic stresses generated by statistically
homogeneous and isotropic turbulence in rigid aggregates, we estimate
theoretically the rate of turbulent breakup of colloidal aggregates and the
size distribution of the formed fragments. The adopted method combines Direct
Numerical Simulation of the turbulent field with a Discrete Element Method
based on Stokesian dynamics. In this way, not only the mechanics of the
aggregate is modelled in detail, but the internal stresses are evaluated while
the aggregate is moving in the turbulent flow. We examine doublets and
cluster-cluster isostatic aggregates, where the failure of a single contact
leads to the rupture of the aggregate and breakup occurs when the tensile force
at a contact exceeds the cohesive strength of the bond. Due to the different
role of the internal stresses, the functional relationship between breakup
frequency and turbulence dissipation rate is very different in the two cases.
In the limit of very small and very large values, the frequency of breakup
scales exponentially with the turbulence dissipation rate for doublets, while
it follows a power law for cluster-cluster aggregates. For the case of large
isostatic aggregates it is confirmed that the proper scaling length for maximum
stress and breakup is the radius of gyration. The cumulative fragment
distribution function is nearly independent of the mean turbulence dissipation
rate and can be approximated by the sum of a small erosive component and a term
that is quadratic with respect to fragment size.
