Nonlinear response of inertial tracers in steady laminar flows: differential and absolute negative mobility

TL;DR

This paper investigates how inertial tracers in laminar flows exhibit complex nonlinear mobility behaviors, including negative differential and absolute mobility, due to inertia-force coupling, with implications for non-equilibrium response theory.

Contribution

It reveals the emergence of negative mobility phenomena in inertial tracers within laminar flows through extensive numerical simulations, highlighting the role of inertia-force coupling in non-equilibrium systems.

Findings

Identification of negative differential mobility in inertial tracers

Observation of absolute negative mobility under certain conditions

Application of generalized Einstein relation to non-equilibrium response

Abstract

We study the mobility and the diffusion coefficient of an inertial tracer advected by a two-dimensional incompressible laminar flow, in the presence of thermal noise and under the action of an external force. We show, with extensive numerical simulations, that the force-velocity relation for the tracer, in the nonlinear regime, displays complex and rich behaviors, including negative differential and absolute mobility. These effects rely upon a subtle coupling between inertia and applied force which induce the tracer to persist in particular regions of phase space with a velocity opposite to the force. The relevance of this coupling is revisited in the framework of non-equilibrium response theory, applying a generalized Einstein relation to our system. The possibility of experimental observation of these results is also discussed.