Passive Microrheology of Strongly Attractive Dense Emulsions using Diffusing Wave Spectroscopy

We make diffusing wave spectroscopy (DWS) measurements of dense, oil-in-water, size-fractionated, colloidal emulsions having strong short-range interdroplet attractions of ~15 k_BT caused by micellar depletion. This strong slippery attraction significantly alters the mean free path of optical transport, l*, compared to nearly hard interactions, and complicates the interpretation of fundamental scattering objects that are associated with DWS self-motion mean square displacements (MSDs), even after accounting for collective scattering. We develop an opto-mechanical decorated core-shell network (DCSN) model to determine an effective radius of the DWS probes by analyzing the measured l*(φ) over a wide range of droplet volume fractions, φ, above and below the hard-sphere jamming point. Using this effective radius and the measured long-time plateau self-motion MSDs, both obtained optically, we show that the generalized Stokes-Einstein relation (GSER) of thermal-entropic passive microrheology yields microrheological plateau elastic shear moduli which are in quantitative agreement with mechanical rheometry.