Abstract

We consider the problem of the derivation of an effective model for viscous dilute suspensions. A previous work by D. Gérard-Varet and M. Hillairet showed that, if a second order Stokes effective approximation exists then the mean value of the second order correction for the effective viscosity is given by a mean-field limit that can be studied and computed under further assumptions on the particle configurations. We extend this result by identifying the second order correction in the general case and show the convergence to the limit effective model as soon as the mean field limit exists. In particular we recover the mean-field analysis considered by D. Gérard-Varet and M. Hillairet in their paper for the homogeneous case of periodic and random stationary particle configurations. This is a joint work with D. Gérard-Varet.