Physics – Condensed Matter – Soft Condensed Matter
Scientific paper
2011-03-11
Phys. Rev. E 84, 021403 (2011)
Physics
Condensed Matter
Soft Condensed Matter
Scientific paper
10.1103/PhysRevE.84.021403
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 $\tau^* \sim (\dot \gamma \Delta \phi^4)^{-1}$ where $\dot\gamma$ is the strain rate and $\Delta\phi=|\phi-\phi_c|$ 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 $n^* \sim (\dot \gamma \Delta \phi^4)^{-0.3}$. Exponent uncertainties are less than ten percent. We emphasize that the same power-law behavior is found at packing fractions above and below $\phi_c$. Thus, our results considerably extend a previous observation of $n^* \sim \dot\gamma^{-0.3}$ for granular heap flow at fixed packing below $\phi_c$. Furthermore, the implied result $n^*\sim (\tau^*)^{0.3}$ compares well with expectation from mode-coupling theory and with prior observations for driven granular systems.
Durian Douglas J.
Gollub J. P.
Nordstrom K. N.
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