Nonlinear Microrheology of Brownian Ellipsoids

Microrheology uses colloidal probes to measure bulk viscoelastic properties of soft materials.  'Passive' microrheology exploits the fluctuation-dissipation theorem to quantitatively recover linear response properties.  However, this theoretical foundation is limited to near-equilibrium behavior, and does hold true for the investigation of nonlinear behavior.  Squires (Langmuir, 2008) discussed a variety of theoretical issues inherent to nonlinear microrheology, including Lagrangian unsteadiness, non-viscometric flows, and inhomogeneous stresses.

To investigate these issues, we have developed a computational system to examine simplest model system that exhibits non-trivial rheology:  a spherical colloidal probe translating through a dilute suspension of rigid ellipsoids or rods.  We explicitly compute the (Lagrangian) transient, spatially-inhomogeneous microstructure in the bulk around the probe, the associated microstructural stresses upon the fluid, and the consequent retarding force upon the probe.  Finally, we examine the effect that these issues have upon the quantitative comparisons between the velocity-dependent "micro-viscosity" and the macroscopically-measured rate-dependent shear viscosity of the same material.