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Mixing in sheared particulate suspensions
The question addressed is how the presence of rigid particles in a viscous shear flow accelerates mixing. High-resolution PIV measurements of the fluid phase were performed to reconstruct the stretching histories of material lines of the interstitial fluid. We found that the nature of the stretching law changes drastically from linear, in absence of particles, to exponential in the presence of particles. The mean and the standard-deviation of the material line elongations are found to grow exponentially in time and the distribution of elongations converges to a log-normal. A multiplicative stretching model, based on the distribution of local shear-rates and on their persistence time, is derived. This model which quantitatively captures the experimental stretching laws provides a complete description of the flow kinematics. Predictions of the mixing times are then inferred showing that the presence of particles accelerates mixing at large Péclet numbers. The wide distribution of stretching rates results in heterogeneous mixing and hence, broadly distributed mixing times.