# Berlin 2015 – wissenschaftliches Programm

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# DY: Fachverband Dynamik und Statistische Physik

## DY 9: Brownian Motion and Transport (Joint session DY/ CPP/ TT)

### DY 9.8: Vortrag

### Montag, 16. März 2015, 17:15–17:30, BH-N 243

**Nonlinear Microrheological response to a step force** — •Thomas Franosch — Institut für Theoretische Physik, Leopold-Franzens-Universität Innsbruck, Innsbruck, Austria

In a microrheological experiment the thermal or forced motion of a colloidal particle is monitored to obtain information on mechanical properties of the surroundings. While the linear response is well-characterized in terms of the fluctuation-dissipation theorem, few exact results are available for strong driving.

Here we consider the time-dependent velocity of a colloidal particle immersed in a dilute suspension of hard spheres in response to switching on a finite constant force. The dimensionless number quantifying the strength of the driving is the Péclet number Pe = *F* σ/*k*_{B} *T*. We present an analytical solution exact to first order in the packing fraction. In particular, we show that at *finite times* the response is an analytic function of the Péclet number, but displays singular behavior for infinite times. Our solution technique extends the stationary state calculation [1] to the time-dependent case. The non-commutitavity of the limits Pe → 0 and time *t*→ ∞ is traced back to the long-time tail in the velocity-autocorrelation function due to repeated encounters with the same colloid. The scenario is strongly reminiscent of a driven particle in a lattice Lorentz model with frozen obstacles [2], and corroborates that linear response becomes qualitatively wrong at long times for arbitrarily small driving.

[1] T.M Squires and J.F. Brady, Phys. Fluids 17, 073101 (2005)

[2] S. Leitmann, T. Franosch, Phys. Rev. Lett. 111, 190603 (2013)