Microrheology of colloidal dispersions: Shape matters

e consider a “probe” particle translating at constant velocity through an otherwise quiescent ispersion of colloidal “bath” particles, as a model for particle-tracking microrheology experiments n the active nonlinear regime. The probe is a body of revolution with major and minor semiaxes and b, respectively, and the bath particles are spheres of radii b. The probe’s shape is such that hen its major or minor axis is the axis of revolution the excluded-volume, or contact, surface etween the probe and a bath particle is a prolate or oblate spheroid, respectively. The moving robe drives the microstructure of the dispersion out of equilibrium; counteracting this is the rownian diffusion of the bath particles. For a prolate or oblate probe translating along its ymmetry axis, we calculate the nonequilibrium microstructure to first order in the volume fraction f bath particles and over the entire range of the Péclet number Pe , neglecting hydrodynamic nteractions. Here, Pe is defined as the non-dimensional velocity of the probe. The microstructure s employed to calculate the average external force on the probe, from which one can infer a microviscosity” of the dispersion via Stokes drag law. The microviscosity is computed as a unction of the aspect ratio of the probe, â=a /b, thereby delineating the role of the probe’s shape. or a prolate probe, regardless of the value of â, the microviscosity monotonically decreases, or velocity thins,” from a Newtonian plateau at small Pe until a second Newtonian plateau is eached as Pe→ . After appropriate scaling, we demonstrate this behavior to be in agreement ith microrheology studies using spherical probes Squires and Brady, “A simple paradigm for ctive and nonlinear microrheology,” Phys. Fluids 17 7 , 073101 2005 and conventional macrorheological investigations Bergenholtz et al., “The non-Newtonian rheology of dilute olloidal suspensions,” J. Fluid. Mech. 456, 239–275 2002 . For an oblate probe, the icroviscosity again transitions between two Newtonian plateaus: for â 3.52 to two decimal laces the microviscosity at small Pe is greater than at large Pe again, velocity thinning ; owever, for â 3.52 the microviscosity at small Pe is less than at large Pe, which suggests it velocity thickens” as Pe is increased. This anomalous velocity thickening—due entirely to the robe shape—highlights the care needed when designing microrheology experiments with nonpherical probes. © 2008 The Society of Rheology. DOI: 10.1122/1.2821894