(4ad) One- and Two-Probe Nonlinear Microrheology: Normal Stress Differences, Osmotic Pressure, and Nonequilibrium Depletion Flocculation

The effect of single- and two-particle motion in nonlinear microrheology is studied, with a view toward connecting microstructural mechanics to normal stress and osmotic pressure. In active microrheology, the motion of a microscale probe (or set of probes) is tracked while being driven by an external force through a colloidal dispersion. Recent work on microrheology has focused on the average motion of a single probe, with the microviscosity defined theoretically and determined experimentally by application of Stokes' drag law. Fluctuations in probe motion are also of interest; collisions between probe and bath particles cause velocity fluctuations, scattering the probe from its mean path. We determined in our recent work that the (long-time) probe scattering is diffusive. The microdiffusivity, D^micro, is transversely anisotropic, scaling linearly in the volume fraction of bath particles φ (for small φ) for all Peclet numbers, Pe, which gives the strength of probe forcing compared to thermal forces: Pe = F^ext/(kT/b), where kT is the thermal energy and b the bath particle size. In light of this anisotropy, the notion that self-diffusion is driven by gradients in the particle or osmotic pressure prompts investigation of normal stresses in active microrheology — the anisotropy of the microdiffusivity indicates the presence of normal stress differences. We take two approaches to determine normal stresses: First, we derive the stresses directly from the deformed microstructure. Second, via the relationship of the microdiffusivity to particle (osmotic) pressure gradients, &partΣ/&partφ, where Σ is the suspension stress. Owing to the axisymmetry of the motion about a spherical probe, N₂ = 0, while N₁ is linear in Pe for Pe >> 1 and vanishes when Pe << 1. The two approaches agree, suggesting that normal stress differences can be measured in active microrheological experiments if both the mean and mean-square motion of the probe are monitored. Next we study anisotropy arising due to external forcing of two probes through the bath — and the corresponding normal stresses. Much work in two-probe microrheology has focused on the linear response regime; here, we investigate the nonlinear response of a colloidal dispersion to the motion of two probe particles, both of size a, kept at constant separation R (scaled by a) and driven at constant velocity U^ext (perpendicular to their line of centres) through the suspension. Brownian dynamics simulations were conducted for concentrated and dilute suspensions, where the probe and bath particles are all of equal size; the bath microstructure and interactive force between probes were measured. The probes attract each other for separations less than a critical value R_c due to the depletion of bath particles between them and repel each other for separations of R_c ≤ R < 4.25 as bath particles are able to accumulate between them. For separations greater than 4.5 radii, the probes no longer interact.