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We consider a suspension of spherical inertialess particles in a Stokes flowon the torus $\mathbb T^3$. The particles perturb a linear extensional flow dueto 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 andDoi models and similar models for active suspensions. The proof of this resultis based on the study of the mobility problem of a single particle in anon-cubic torus, which we prove to exhibit a nontrivial coupling between theangular velocity and a prescribed strain.

Non-existence of mean-field models for particle orientations in suspensions