Active and Nonlinear Microrheology in Dense Colloidal Suspensions

We present a first-principles theory for the active nonlinear microrheology of colloidal model system; for a constant external force on a spherical probe particle embedded in a dense host dispersion, neglecting hydrodynamic interactions, we derive an exact expression for the friction. Within mode-coupling theory, we discuss the threshold external force needed to delocalize the probe from a host glass, and its relation to strong nonlinear velocity-force curves in a host fluid. Experimental microrheology data and simulations, which we performed, are explained with a simplified model.

Figure 1

Circles: Threshold force $F_c^{\mathrm{ex}}(\phi )$ needed to delocalize a hard-sphere probe particle in a glass of equally large hard spheres with packing fraction $\phi$ above the glass transition (dotted line), calculated from MCT within the Percus-Yevick approximation. Crosses mark $F^{\mathrm{ex}}$ values used in Fig. 2. Inset: corresponding schematic-model result for $v_s=4$ (see text).

Figure 2

Contour plot of the probability distribution $f^s(\mathit{r})$ for a localized hard-sphere probe of radius $a$ in a hard-sphere system with same radius at $\phi =0.52$, for external forces acting to the right with indicated magnitude in units of $k_{B}T/a$.

Figure 3

(a) Probe friction $\zeta$ as a function of external force for packing fractions $\phi$ as indicated, from simulations of a quasi-hard-sphere system (filled symbols), from Brownian dynamics for monodisperse HS (Ref. 17, open symbols). (b) Experimental force-velocity relations for a colloidal suspension, from Ref. 5 (open symbols). Lines: fits using the schematic model (see text and Ref. 12 for parameters); common rescaling factors for force and friction increment ($\zeta -{\zeta }_s$) are $17.9k_{B}T/a$ and $0.29{\zeta }_s$ (left panel), 0.06 pN and $0.19{\zeta }_s$ (right panel).

Figure 4

Probe-particle density correlation function ${\varphi }_{\mathit{q}}^s(t)$ from computer simulation at $\phi =0.55$ (left) and from schematic MCT (right; fit as in Fig. 3), real (top) and imaginary (bottom) parts. $\mathit{q}\parallel {\mathit{F}}^{\mathrm{ex}}$ corresponds to the position of the main peak in the static structure factor $S(q)$. For the simulation, $a{F}^{\mathrm{ex}}/(k_{B}T)=1$, 10, 20, 30, 50, 100, and 250 (right to left).