Dynamical heterogeneity in soft particle suspensions under shear

We present experimental measurements of dynamical heterogeneities in a dense system of microgel spheres, sheared at different rates and at different packing fractions in a microfluidic channel, and visualized with high speed digital video microscopy. A four-point dynamic susceptibility is deduced from video correlations, and is found to exhibit a peak that grows in height and shifts to longer times as the jamming transition is approached from two different directions. In particular, the time for particle-size root-mean square relative displacements is found to scale as $τ^* \sim (\dot γΔϕ^4)^{-1}$ where $\dotγ$ is the strain rate and $Δϕ=|ϕ-ϕ_c|$ is the distance from the random close packing volume fraction. The typical number of particles in a dynamical heterogeneity is deduced from the susceptibility peak height and found to scale as $n^* \sim (\dot γΔϕ^4)^{-0.3}$. Exponent uncertainties are less than ten percent. We emphasize that the same power-law behavior is found at packing fractions above and below $ϕ_c$. Thus, our results considerably extend a previous observation of $n^* \sim \dotγ^{-0.3}$ for granular heap flow at fixed packing below $ϕ_c$. Furthermore, the implied result $n^*\sim (τ^*)^{0.3}$ compares well with expectation from mode-coupling theory and with prior observations for driven granular systems.

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