Probe Mobility in Finite Stokes Number Suspensions: From Viscous to Granular Microrheology

Microrheology – whereby viscoelastic properties of a complex fluid are inferred from the motion of a small, immersed probe – has emerged as a useful tool for studying suspensions, particularly those systems that are too small for traditional techniques. In this small limit, particle inertia is typically negligible. Microrheology, however, may be an equally valuable paradigm for larger, inertial suspensions such as granular flows, where micro-scale phenomena underly processes like mixing and segregation. In this talk, we outline a framework for passive and active microrheology in sheared, finite Stokes number suspensions, thus connecting the non-inertial and inertial limits. In the small Stokes regime (non-inertial), probe mobility is characterized by a competition between forcing and shearing, resulting in force-thinning behavior under passive forcing that gives way to a viscous plateau under active forcing. By contrast, in the large Stokes (inertial, or granular) regime – characterized by competition between forcing and collision-induced diffusion – microviscosity is constant for passive forcing, and force thickens as Pe² under active forcing. Particle dynamics results for a large range of Stokes numbers, volume fractions, and elastic coefficients collapse predictably as a function of Peclet number and shear rate-normalized forcing in the high and low Stokes regimes, respectively.