Berlin 2015 – scientific programme

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TT: Fachverband Tiefe Temperaturen

TT 25: Brownian Motion and Transport (jointly with DY, CPP)

TT 25.8: Talk

Monday, March 16, 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)