Micro–macro-discrepancies in nonlinear microrheology: I. Quantifying mechanisms in a suspension of Brownian ellipsoids

Abstract

Active and nonlinear microrheology experiments involve a colloidal probe that is forced to move within a material, with the goal of recovering the nonlinear rheological response properties of the material. Various mechanisms cause discrepancies between the nonlinear rheology measured microrheologically and macroscopically, including direct probe-bath collisions, the Lagrangian unsteadiness experienced by the material elements, and the spatially inhomogeneous and rheologically mixed strain field set up around the probe. Here, we perform computational nonlinear microrheology experiments, in which a colloidal probe translates through a dilute suspension of Brownian ellipsoids, whose results we compare against analogous computational experiments on the macroscopic shear rheology of the same model material. The quantitative impact of each of the mechanisms for micro-macro-discrepancy can thus be computed directly, with additional computational experiments performed where the processes in question are 'turned off'. We show that all three discrepancy mechanisms impact the microrheological measurement quantitatively, and that none can be neglected. This motivates a search for microrheological probes whose geometry or forcing is optimized to minimize these impacts, which we present in a companion article.

The impact of hydrodynamics on viscosity evolution in colloidal dispersions: Transient, nonlinear microrheology

“…More fundamentally, it provides a compelling connection between fluctuation and dissipation away from equilibrium, extending Einstein's equilibrium fluctuation‐dissipation theory of Brownian motion to strong departures from equilibrium (H. C. W. Chu and R. N. Zia, in preparation). Experimental studies, theoretical models, and dynamic simulations of active microrheology have recovered steady‐state non‐Newtonian behaviors measured via traditional shear rheology, including flow thinning and thickening, flow‐induced diffusion, normal stress differences, and linear viscoelasticity . Comparison between rheological measurements obtained via viscometric flows, for example, simple shear, and those obtained via microrheology, reveal many qualitative similarities as well as important differences.…”

Transient dynamics of a colloidal particle driven through a viscoelastic fluid

“…More-complex transient behavior observed macroscopically, e.g., nonlinear creep, stress relaxation, and strain recovery, is far less well-understood within the context of microrheology. Indeed, theoretical works suggest that the drag force acting on a colloidal probe driven through a non-Newtonian fluid strongly depends on the spatio-temporal deformation of the microstructure of the surrounding fluid [29][30][31]. Therefore, in contrast to Newtonian liquids, where a low Reynolds number guarantees simple Stokesian flows and linear-response drag forces, it is questionable whether this is applicable when a particle is dragged by a time-dependent driving force over large distances through a viscoelastic medium [32].…”

Diffusion microrheology of ferrofluids

“…Tracking microrheology experiments are useful techniques that accurately provide the linear viscoelasticity of suspensions of polystyrene particles and other complex fluids [5,7,34,35]. In these experiments it is assumed that the complex shear moduli can be determined from the particle's mean squared displacement in the linear regime of low shear flow.…”