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

TL;DR

This paper investigates the nonlinear force-velocity behavior of inertial tracers in laminar flows, revealing phenomena like negative differential mobility and absolute negative mobility through extensive numerical simulations.

Contribution

It provides a detailed phase diagram of inertial tracer responses, highlighting conditions for anomalous mobility effects in laminar flow environments.

Findings

Identification of parameter regions with negative differential mobility

Discovery of conditions leading to absolute negative mobility

Mapping of the force-velocity response behaviors

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 $\tau$ 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, $(\tau,D_0)$, identifying the regions where NDM, ANM and more common monotonic behaviors of the force-velocity curve are observed.