Universal and Non-Universal First-Passage Properties of Planar Multipole Flows

TL;DR

This paper investigates the first-passage properties of passive particles in 2D potential flows, revealing universal and non-universal behaviors depending on flow type, with implications for understanding particle transport in complex flow fields.

Contribution

It introduces a comprehensive analysis of first-passage probabilities in multipolar flows, highlighting new decay behaviors and spatial distribution invariances.

Findings

Power-law decay of first-passage probability with flow-dependent exponents

Existence of diffusive 'echo' shoulders and exponential decays near stagnation points

Spatial distribution independence from flow magnitude for dipole sinks

Abstract

The dynamics of passive Brownian tracer particles in steady two-dimensional potential flows between sources and sinks is investigated. The first-passage probability, $p(t)$, exhibits power-law decay with a velocity-dependent exponent in radial flow and an order-dependent exponent in multipolar flows. For the latter, there also occur diffusive ``echo'' shoulders and exponential decays associated with stagnation points in the flow. For spatially extended dipole sinks, the spatial distribution of the collected tracer is independent of the overall magnitude of the flow field.