Active microrheology: a proposed technique to measure normal stress coefficients of complex fluids

We propose a microrheological technique to measure normal stress coefficients (NSCs) of complex fluids, which would represent the first quantitatively accurate measurement of a nonlinear rheological property by microrheology. Specifically, the mechanical response of almost all complex fluids to "weakly nonlinear" deformations is described by the second-order fluid model. Two microrheological probes pulled with equal velocities through a second-order fluid experience a relative force that is linear in the first and second NSCs of the complex fluid. We compute the coupling matrix between NSCs and relative forces for probes translating parallel and perpendicular to their line of centers, which can be inverted to yield NSCs from measured relative forces. There exists an optimum probe separation for inversion of the coupling matrix and, hence, experimental recovery of NSCs.