Field-driven tracer diffusion through curved bottlenecks: Fine structure of first passage events

TL;DR

This study investigates how a tracer particle moves through curved bottlenecks in a channel, revealing detailed first passage behaviors and sensitivities overlooked by traditional models.

Contribution

It provides a detailed analysis of first passage distributions in curved bottlenecks, highlighting new dynamical features beyond the Fick-Jacobs approximation.

Findings

Trajectories concentrate on funnel boundaries

First-crossing events are highly sensitive to boundary roughness

New features of tracer dynamics in corrugated channels

Abstract

Using scaling arguments and extensive numerical simulations, we study dynamics of a tracer particle in a corrugated channel represented by a periodic sequence of broad chambers and narrow funnel-like bottlenecks enclosed by a hard-wall boundary. A tracer particle is affected by an external force pointing along the channel, and performs an unbiased diffusion in the perpendicular direction. We present a detailed analysis a) of the distribution function of the height above the funnel's boundary at which the first crossing of a given bottleneck takes place, and b) of the distribution function of the first passage time to such an event. Our analysis reveals several new features of the dynamical behaviour which are overlooked in the studies based on the Fick-Jacobs approach. In particular, trajectories passing through a funnel concentrate predominantly on its boundary, which makes first-crossing events very sensitive to the presence of binding sites and a microscopic roughness.