Microrheology of colloidal dispersions by Brownian dynamics simulations

We investigate active particle-tracking microrheology in a colloidal dispersion by Brownian dynamics simulations. A probe particle is dragged through the dispersion with an externally imposed force in order to access the nonlinear viscoelastic response of the medium. The probe’s motion is governed by a balance between the external force and the entropic “reactive” force of the dispersion resulting from the microstructural deformation. A “microviscosity” is defined by appealing to the Stokes drag on the probe and serves as a measure of the viscoelastic response. This microviscosity is a function of the Péclet number $(Pe=Fa∕kT)$—the ratio of “driven” $(F)$ to diffusive $(kT∕a)$ transport—as well as of the volume fraction of the force-free bath particles making up the colloidal dispersion. At low Pe—in the passive microrheology regime—the microviscosity can be directly related to the long-time self-diffusivity of the probe. As Pe increases, the microviscosity “force-thins” until another Newtonian plateau is reached at large Pe. Microviscosities for all Péclet numbers and volume fractions can be collapsed onto a single curve through a simple volume fraction scaling and equate well to predictions from dilute microrheology theory. The microviscosity is shown to compare well with traditional macrorheology results (theory and simulations).