  Breakup of small solid aggregates in homogeneous and isotropic turbulence is
studied theoretically and by using Direct Numerical Simulations at high
Reynolds number, Re_{\lambda} \simeq 400. We show that turbulent fluctuations
of the hydrodynamic stress along the aggregate trajectory play a key role in
determining the aggregate mass distribution function. Differences between
turbulent and laminar flows are discussed. A novel definition of the
fragmentation rate is proposed in terms of the typical frequency at which the
hydrodynamic stress becomes sufficiently high to cause breakup along each
Lagrangian path. We also define an Eulerian proxy of the real fragmentation
rate, based on the joint statistics of the stress and its time derivative,
which should be easier to measure in any experimental set-up. Both our Eulerian
and Lagrangian formulations define a clear procedure for the computation of the
mass distribution function due to fragmentation. Contrary, previous estimates
based only on single point statistics of the hydrodynamic stress exhibit some
deficiencies. These are discussed by investigating the evolution of an ensemble
of aggregates undergoing breakup and aggregation.
