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^*∼(γ˙Δφ⁴)^-1, where γ˙ 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^*∼(γ˙Δφ⁴)^-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^*∼γ˙^-0.3 for granular heap flow at fixed packing below φ_c. Furthermore, the implied result n^*∼(τ^*)^0.3 compares well with the expectation from mode-coupling theory and with prior observations for driven granular systems.