[Analyse d’une suspension de particules en sédimentation à proximité d’une paroi verticale]
We consider a sedimenting suspension in a Stokes flow, in the presence of a vertical wall. We study the effect of a particle-depleted fluid layer near the wall on the bulk dynamics of the suspension. We show that this effect can be captured by an appropriate wall law of Navier type. Under appropriate lower bound for the minimal distance and the size of the depletion layer, we provide in this way a rigorous justification of the apparent slip observed in many experiments. We also discuss the phenomenon of intrinsic convection predicted in some physics articles.
Nous considérons des particules sédimentant dans un fluide de Stokes en la présence d’une paroi verticale. Nous étudions l’effet du bord ainsi que de la couche limite appauvrie en particules sur la dynamique de la suspension. Nous montrons que cet effet peut être modélisé par des conditions au bord de type Navier. Sous certaines hypothèses concernant la distance minimale entre particules ainsi que la taille de la couche limite, nous proposons une justification rigoureuse du phénomène de glissement apparent observé dans certaines expériences. Nous discutons également du phénomène de convection intrinsèque étudié dans certains articles de physique.
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Keywords: Sedimentation of particles, Stokes flow, method of reflections, boundary layer analysis
Mots-clés : Sédimentation de particules, fluide de Stokes, méthode de réflexions, analyse de type couche limite
David Gérard-Varet 1 ; Amina Mecherbet 1
CC-BY 4.0
@article{JEP_2025__12__523_0,
author = {David G\'erard-Varet and Amina Mecherbet},
title = {Analysis of a sedimenting suspension near a~vertical wall},
journal = {Journal de l{\textquoteright}\'Ecole polytechnique {\textemdash} Math\'ematiques},
pages = {523--546},
publisher = {\'Ecole polytechnique},
volume = {12},
year = {2025},
doi = {10.5802/jep.296},
language = {en},
url = {https://jep.centre-mersenne.org/articles/10.5802/jep.296/}
}
TY - JOUR AU - David Gérard-Varet AU - Amina Mecherbet TI - Analysis of a sedimenting suspension near a vertical wall JO - Journal de l’École polytechnique — Mathématiques PY - 2025 SP - 523 EP - 546 VL - 12 PB - École polytechnique UR - https://jep.centre-mersenne.org/articles/10.5802/jep.296/ DO - 10.5802/jep.296 LA - en ID - JEP_2025__12__523_0 ER -
%0 Journal Article %A David Gérard-Varet %A Amina Mecherbet %T Analysis of a sedimenting suspension near a vertical wall %J Journal de l’École polytechnique — Mathématiques %D 2025 %P 523-546 %V 12 %I École polytechnique %U https://jep.centre-mersenne.org/articles/10.5802/jep.296/ %R 10.5802/jep.296 %G en %F JEP_2025__12__523_0
David Gérard-Varet; Amina Mecherbet. Analysis of a sedimenting suspension near a vertical wall. Journal de l’École polytechnique — Mathématiques, Tome 12 (2025), pp. 523-546. doi : 10.5802/jep.296. https://jep.centre-mersenne.org/articles/10.5802/jep.296/
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