Solutions to the Stokes problem for particles suspended in a moving fluid express mathematically their active (nonaffine) advection. A mesoscopic model of the microhydrodynamic formulation of the advection is developed and its rheological consequences are investigated. The model is constructed as a particular realization of a framework (GENERIC) guaranteeing the compatibility of dynamics with thermodynamics. (C) 2007 Elsevier B.V. All rights reserved.