Related Experiment Video
Updated: Jun 28, 2026

The Diffusion of Passive Tracers in Laminar Shear Flow
Published on: May 1, 2018
Localization and spectral phase transition in an open advecting-diffusing three-dimensional Stokes flow
1Dipartimento di Ingegneria Chimica, Università di Roma La Sapienza, via Eudossiana 18, 00184 Roma, Italy. max@giona.ing.uniroma1.it
Abstract:
We study the steady-state characterization of an advecting-diffusing three-dimensional flow defined in the annular region between coaxial cylinders of finite length that can rotate independently. A phase transition occurs when the cylinder velocities vary, which controls the spectral properties of the dominant eigenvalue and eigenfunction of the advection-diffusion equation for high Péclet numbers. The localization abscissa of the dominant eigenfunction can be used as the order parameter of the transition, and is a continuous function of the wall velocity. Conversely, the exponent characterizing the scaling of the real part of the dominant eigenvalue displays a discontinuous behavior at the critical point. Theoretical arguments support the localization properties observed numerically and provide a simple explanation of this phenomenon.
Related Concept Videos
Divergence and Stokes' Theorems
Stokes' Law
The expression for the force on a solid spherical object in a fluid is called Stokes' law. Stokes' law is valid only for low Reynolds...
Navier–Stokes Equations
Bernoulli's Equation for Flow Along a Streamline
Bernoulli's Equation for Flow Normal to a Streamline
The pressure difference depends on the fluid's velocity and radius of curvature. The pressure variation is minimal in flows with nearly straight streamlines. However, the...
Steady, Laminar Flow in Circular Tubes

