(279e) One and Two-Point Active and Nonlinear Microrheology
In passive microrheology (Mason & Weitz), the thermal fluctuations of a passive tracer colloid are measured and directly related to the linear viscoelastic properties of the surrounding material. Direct physical and chemical interactions betwen the probe particle and the material that surrounds it are known to cause discrepancies between micro- and macro-rheological measurements. So-called two point microrheology, in which correlated fluctuations between multiple probes are measured, have been shown to reduce the sensitivity of passive microrheological measurement to probe-material interaction artifacts (J. Crocker et al., Levine & Lubensky). Here we explicitly compute the one- and two-point linear microrheological response of large probe(s) in a dilute colloidal suspension, for which the microstructural deformations and therefore rheology can be determined explicitly. We demonstrate indeed that the direct probe-material interactions give rise to additional rheological features in one-point measurements that have no rheological analog, and that two-point techniques are much less sensitive to these features. We then discuss active and (slightly) nonlinear microrheology, where the analogous probe-bath interactions give rise to analogous features that have no analog in macroscopic steady shear rheology. Finally, we demonstrate that the normal stress coefficients N_1 and N_2 can be measured using active two-point methods, and that such results agree quantitatively with the corresponding macrorheology, giving the first example in which a nonlinear rheological quantity can be captured microrheologically.