Modeling the microrheology of inhomogeneous media

We model the restricted diffusion of small tracer particles near a gel transition by performing Monte Carlo simulations in a site-percolation model. From the mean squared displacement of the particles, we calculate the effective viscous and elastic moduli using the microrheological equations derived from the generalized Stokes–Einstein relation by Mason [T.G. Mason, Rheol. Acta 39 (2000) 371]. The results show a transition from viscous to elastic behavior at a site-filling probability that is different from that at the percolation transition, and that occurs at higher site-filling probability for smaller tracer particles. This behavior is due to confinement of the tracers in the inhomogeneous system, and we discuss the inapplicability of the generalized Stokes–Einstein relation in this case. The simulations are in partial agreement with experimental results obtained for a gelling clay suspension and polymer blends, but there are also differences which suggest the importance of microstructure, and specifically elastic effects in the experimental systems. We discuss the implications of our simulations for the interpretation of microrheological experiments on inhomogeneous media.

► Model diffusion of particles in a material near its gel point.
► Study the effects of particle confinement on effective local moduli.
► Use the model results to aid in the interpretation of recent experiments.