Mixing viscous fluids is difficult. The question addressed here is how the presence of rigid particles in a viscous shear flow accelerates this process. High-resolution PIV measurements of the fluid phase are performed to reconstruct the stretching histories of material lines of the interstitial fluid. We find that the nature of the stretching law changes drastically from linear, in absence of particles, to exponential in the presence of particles. After a complete characterization of the fluid flow kinematics, we can predict the mixing process, and in particular, the evolution of the concentration distribution of a blob of fluorescent dye injected in the sheared suspension. Collaborators: Mathieu Souzy, Regis Turuban, Emmanuel Villermaux, Henri Lhuissier Refs: (2017) Stretching and mixing in sheared particulate suspensions J. Fluid Mech. - (2018) Mixing lamellae in a shear flow J. Fluid Mech. - (2020) Velocity distributions, dispersion and stretching in three-dimensional porous media. J. Fluid Mech. - (2021) Mixing in a sheared particulate suspension J. Fluid Mech.