Active and Passive Microrheology: Theory and Simulation

Abstract

Microrheological study of complex fluids traces its roots to the work of the botanist Robert Brown in the early nineteenth century. Indeed, passive microrheology and Brownian motion are one and the same. Once thought to reveal a fundamental life force, the phenomenon was ultimately leveraged by Einstein in proof of the atomic nature of matter ( Haw 2006 ). His work simultaneously paved the way for modern-day passive microrheology by connecting observable particle motion—diffusion—to solvent properties—the viscosity—via the well-known Stokes–Einstein relation. Advances in microscopy techniques in the last two decades have prompted extensions of the original model to generalized forms for passive probing of complex fluids. In the last decade, active microrheology has emerged as a means by which to interrogate the nonequilibrium behavior of complex fluids, in particular, the non-Newtonian rheology of dynamically heterogeneous and microscopically small systems. Here we review theoretical and computational approaches and advances in both passive and active microrheology, with a focus on the extent to which these techniques preserve the connection between single-particle motion and flow properties, as well as the rather surprising recovery of non-Newtonian flow behavior observed in bulk rheology.