On the derivation of viscoelastic models for Brownian rod-like suspensions

We consider effective properties of suspensions of inertialess, rigid, anisotropic, Brownian particles in Stokes flows. Recent years have seen tremendous progress regarding the rigorous justification of effective fluid equations for non-Brownian suspensions, where the complex fluid can be described in terms of an effective viscosity. In contrast to this (quasi-)Newtonian behavior, anisotropic Brownian particles cause an additional elastic stress on the fluid which leads to a variety of fascinating phenomena. A rigorous derivation of viscoelastic fluid systems starting from particle models is completely missing so far. In this talk I will present first results in this direction starting from a simplified microscopic model where the particles evolve only due to rotational Brownian motion and cause a Brownian torque on the fluid. In the limit of infinitely many small particles with very small particle volume fraction, we rigorously obtain an elastic stress on the fluid in terms of the particle density that is given as the solution to an (in-)stationary Fokker-Planck equation.

Joint work with Marta Leocata (Scuola Normale Superiore Pisa) and Amina Mecherbet (Université Paris Cité)