  We consider a suspension of spherical inertialess particles in a Stokes flow
on the torus $\mathbb T^3$. The particles perturb a linear extensional flow due
to their rigidity constraint. Due to the singular nature of this perturbation,
no mean-field limit for the behavior of the particle orientation can be valid.
This contrasts with widely used models in the literature such as the FENE and
Doi models and similar models for active suspensions. The proof of this result
is based on the study of the mobility problem of a single particle in a
non-cubic torus, which we prove to exhibit a nontrivial coupling between the
angular velocity and a prescribed strain.
