Starting from microscopic
-particle
systems, we study the derivation of Doi-type models for suspensions of nonspherical
particles in Stokes flows. While Doi models accurately describe the effective evolution
of the spatial particle density to the first order in the particle volume fraction,
this accuracy fails regarding the evolution of the particle orientations. We
rigorously attribute this failure to the singular interaction of the particles via a
-homogeneous
kernel. In the situation that the particles are initially distributed according
to a stationary ergodic point process, we identify the limit of this singular
interaction term. It consists of two parts. The first corresponds to a classical term
in Doi-type models. The second new term depends on the (microscopic)
-point
correlation of the point process. By including this term, we provide a modification of
the Doi model that is accurate to first order in the particle volume fraction.
Keywords
fluid mechanics, Doi model, suspension, homogenization,
mean-field limit
