An Active Microrheological Technique to Determine Normal Stress Differences of Complex Fluids

Passive microrheology is a popular technique for measuring the linear-response rheological properties of complex fluids, through the fluctuating motion of embedded colloidal probes. Active microrheology, in contrast, aims to infer non-linear rheological information using actively driven probes. Presently, however, the focus of active microrheology has been limited to attempting to extract the material viscosity as a function of driving speed. In this talk, we propose a new active microrheological technique to determine both the first (N₁) and second (N₂) normal stress differences of a complex fluid, a task which is notoriously difficult in macroscopic mechanical rheometry. Specifically, we consider a two-point active microheology "experiment" in which a pair of colloidal probes are driven with constant velocity through a second order fluid --- the prototypical model for a large class of complex fluids in the limit of gentle deformations. We calculate the relative forces acting on the probes as they are pulled parallel and perpendicular to their line of centres, from which N₁ and N₂ are determined. Finally, we discuss the experimental feasibility of the proposed technique.