Active and Nonlinear Microrheology of Complex Materials

While materials are most commonly thought of as solids, liquids, or gasses, a tremendous variety of everyday materials (biological materials, consumer care products, foods, etc.) elude such easy classification. Rather, they fall somewhere in between -- e.g. solids on short time scales and fluids on long time scales. Over many decades, techniques in rheology have been developed to study how such materials deform and flow. Conventional rheology is 'macroscopic', in the sense that it requires milliliter quantities for analysis. Many materials, however, would be too difficult, too expensive, or impossible to procure in the amounts required for such (macro-) rheometry. In the past decade, "microrheology" has been developed to study such materials. Rather than externally forcing a macroscopic quantity of the material, small colloidal beads are introduced and driven into (Brownian) motion by thermal forces. Because the material remains in (or close to) equilibrium, the (frequency-dependent) linear-response properties of the material can be obtained from the fluctuating probe motion using the fluctuation- dissipation theorem. This, however, suggests another limit to microrheology -- nonlinear material properties (shear thickening or thinning, yield stresses, and so on) can not be obtained using conventional techniques. Here we will discuss recent experiments in which the colloidal probe is actively driven through the material in order to probe its nonlinear response. We will address various theoretical issues in such studies -- most crucially, what exactly is being measured, and how might these measurements be interpreted to give the material information one desires?