Watch a blob of dye advected and stretched by vortical flow. The Péclet number Pe = UL/D measures advection vs diffusion: at high Pe the flow stretches the dye into fine filaments before diffusion can blur them, creating efficient mixing. At low Pe, diffusion dominates and smears the dye uniformly.
316
1.0
0.8
3000
Advection-diffusion equation: ∂c/∂t + u·∇c = D∇²c
Péclet number:Pe = UL/D — ratio of advective to diffusive transport.
At Pe ≫ 1: advection dominates, dye stretched into filaments (chaotic advection when flow is time-dependent).
At Pe ≪ 1: diffusion dominates, concentration spreads isotropically.
Chaotic advection (Aref 1984): Even smooth, laminar flows can generate chaotic particle trajectories when the flow is time-dependent or 3D, leading to exponential stretching and efficient mixing — the Lyapunov exponent controls the mixing rate.