Stretching and mixing in sheared particulate suspensions

Abstract

We experimentally investigate mixing in sheared particulate suspensions by measuring a crucial kinematic quantity of the flow: the stretching laws of material lines in the suspending liquid. High-resolution particle image velocimetry (PIV) measurements in the fluid phase are performed to reconstruct, following the Diffusive Strip Method (Meunier & Villermaux, J. Fluid Mech., vol. 662, 2010, pp. 134–172), the stretching histories of the fluid material lines. In a broad range of volume fractions $20\,\%\leqslant \unicode[STIX]{x1D719}\leqslant 55\,\%$, the nature of the elongation law changes drastically from linear, in the 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 quantitatively captures the experimental stretching laws. The presence of particles is shown to accelerate mixing at large Péclet numbers (${\gtrsim}10^{5}$). However, the wide distribution of stretching rates results in heterogeneous mixing and, hence, broadly distributed mixing times, in qualitative agreement with experimental observations.