Force induced microdiffusivity of colloidal particles

\newcommand{\te}[1]{\mbox{\boldmath$ #1 $}} In constant force microrheology the velocity of the probe particle fluctuates owing to interactions with the surrounding medium. On long time scales, this fluctuating velocity gives rise to a diffusive motion of the probe particle. We study this diffusive motion as the Peclet number, $Pe$ -- the ratio of the strength of the external driving force, $\te{F}^{ext}$, compared to thermal forces, $kT/a$ -- is varied. Here, $kT$ is the thermal energy and $a$ the probe size. At small $Pe$, Brownian motion dominates and the diffusive behavior characteristic of passive microrheology is recovered. At the other extreme of high Peclet numbers the motion is still diffusive, and the diffusivity becomes ``force-induced'' scaling as $\te{F}^{ext}/\eta$, where $\eta$ is the viscosity of the solvent. Specific calculations are performed for a probe particle of size $a$ immersed in a background of colloidal bath particles of size $b$. The diffusive motion becomes increasingly anisotropic as the Peclet number is increased -- motion parallel to the direction of forcing exceeding that transverse. The ``force-induced'' microdiffusivity is compared with the analogous ``shear-induced'' diffusivity found in macrorheological measurements.