Diffusion in a fluid flow generated by a source at the apex of a wedge

TL;DR

This paper analyzes how particles diffuse within a wedge-shaped region under radial fluid flow, revealing that survival probability decay depends on geometric and flow parameters, with implications for understanding fluid-particle interactions.

Contribution

It introduces a novel approach linking diffusion decay exponents to quantum ground state energies in shaped potential wells influenced by flow conditions.

Findings

Decay exponent depends on wedge angle and Reynolds number

Survival probability follows a power-law decay over time

Ground state energy analogy provides a new computational method

Abstract

We consider a particle diffusing inside a wedge with absorbing boundaries and driven by a radial flow of incompressible fluid generated by a source at the apex. The survival probability decays as (time)^{-b} with exponent depending on the opening angle of the wedge and the Reynolds number associated with the hydrodynamic flow. The computation of the decay exponent reduces to finding the ground state energy of the quantum particle in an infinitely deep potential well with shape determined by the radial flow velocity.