Anomalous force-velocity relation of driven inertial tracers in steady laminar flows

Abstract

We study the nonlinear response to an external force of an inertial tracer advected by a two-dimensional incompressible laminar flow and subject to thermal noise. In addition to the driving external field $F$, the main parameters in the system are the noise amplitude $D_0$ and the characteristic Stokes time $τ$ of the tracer. The relation velocity vs force shows interesting effects, such as negative differential mobility (NDM), namely a non-monotonic behavior of the tracer velocity as a function of the applied force, and absolute negative mobility (ANM), i.e. a net motion against the bias. By extensive numerical simulations, we investigate the phase chart in the parameter space of the model, $(τ,D_0)$, identifying the regions where NDM, ANM and more common monotonic behaviors of the force-velocity curve are observed.

5 pages, 13 figures. Contribution to the Topical Issue "Fluids and Structures: Multi-scale coupling and modeling", edited by Luca Biferale, Stefano Guido, Andrea Scagliarini, Federico Toschi. The final publication is available at Springer via http://dx.doi.org/10.1140/epje/i2017-11571-y