Scalar mixing by stagnation points on solid surfaces
Abstract
Recent advances have linked mixing in porous media to the deformation of infinitesimal fluid elements. However, these Lagrangian frameworks generally neglect or simplify interactions with solid surfaces. We consider transport of thin solute blobs (strips or sheets) near single generic obstacles, in particular along separation lines (separatrices) which connect to stagnation points at solid boundaries. In this case, we demonstrate that the coupling between flow and diffusion is analytically tractable. We provide a complete theory for scalar mixing near upstream stagnation points, which we validate by numerical simulations. We identify a mixing time scale tB ∼ Pe1/3, where Pe is the Péclet number, which controls whether scalar decay is driven by fluid stretching or by interaction with the solid boundary. Asymptotically, for times t < tB, we find that the maximum concentration cmax decays as t−5/2 and that the width σ grows like t1/2. For t > tB, we find exponential decay of cmax and constant width σ∼ sB ∼ Pe−1/3, where sB is a mixing length scale distinct from that which appears in shear flows. The asymptotic scalings of cmax(t) and σ(t), and their dependence on Pe, are universal to no-slip stagnation points and qualitatively different from stagnation points in open flows.
Related
- Scalar Laplace-Beltrami harmonics and curvature-induced radial mode mixing in Friedmann-like cosmologies
- Scalar glueball-ss̅ mixing in one flavor lattice QCD
- Scalar gradient structure and dynamics in turbulent mixing at high Reynolds and Schmidt numbers
- Premixed flames in a stagnation point flow under Darcy's law
- How stagnation lines move, persist and break up in fluid flows
BibTeX
@misc{linga2026scalar,
title = {{Scalar mixing by stagnation points on solid surfaces}},
author = {Gaute Linga and Tanguy Le Borgne and Joris Heyman},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.00790},
eprint = {2610.00790},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.00790},
}
RIS
TY - UNPB
TI - Scalar mixing by stagnation points on solid surfaces
AU - Gaute Linga
AU - Tanguy Le Borgne
AU - Joris Heyman
PY - 2026
DA - 2026/10/01
PB - arXiv
DO - 10.48550/arxiv.2610.00790
UR - https://arxiv.org/abs/2610.00790
AB - Recent advances have linked mixing in porous media to the deformation of infinitesimal fluid elements. However, these Lagrangian frameworks generally neglect or simplify interactions with solid surfaces. We consider transport of thin solute blobs (strips or sheets) near single generic obstacles, in particular along separation lines (separatrices) which connect to stagnation points at solid boundaries. In this case, we demonstrate that the coupling between flow and diffusion is analytically tractable. We provide a complete theory for scalar mixing near upstream stagnation points, which we validate by numerical simulations. We identify a mixing time scale t_B ∼ Pe^1/3, where Pe is the Péclet number, which controls whether scalar decay is driven by fluid stretching or by interaction with the solid boundary. Asymptotically, for times t < t_B, we find that the maximum concentration c_max decays as t^−5/2 and that the width σ grows like t^1/2. For t > t_B, we find exponential decay of c_max and constant width σ∼ s_B ∼ Pe^−1/3, where s_B is a mixing length scale distinct from that which appears in shear flows. The asymptotic scalings of c_max(t) and σ(t), and their dependence on Pe, are universal to no-slip stagnation points and qualitatively different from stagnation points in open flows.
ER -