We extend the lubrication approximation for a viscous flow in two-dimensional channels with arbitrary shape functions and moderate aspect ratio. The higher-order model is obtained following an asymptotic analysis. Velocity and pressure profiles for the approximated model are given analytically and involve the derivatives of the shape functions of the walls up to the second order. Comparisons with full-scale simulations are given and show good agreement as well as improvements from the classical standard lubrication approximation.
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@article{CRMECA_2019__347_5_389_0,
author = {Rogers Bill Cordova Hinojosa and Kim Pham and Corinne Rouby},
title = {Extension of the lubrication theory for arbitrary wall shape: {An} asymptotic analysis},
journal = {Comptes Rendus. M\'ecanique},
pages = {389--396},
publisher = {Elsevier},
volume = {347},
number = {5},
year = {2019},
doi = {10.1016/j.crme.2019.03.016},
language = {en},
}
TY - JOUR AU - Rogers Bill Cordova Hinojosa AU - Kim Pham AU - Corinne Rouby TI - Extension of the lubrication theory for arbitrary wall shape: An asymptotic analysis JO - Comptes Rendus. Mécanique PY - 2019 SP - 389 EP - 396 VL - 347 IS - 5 PB - Elsevier DO - 10.1016/j.crme.2019.03.016 LA - en ID - CRMECA_2019__347_5_389_0 ER -
%0 Journal Article %A Rogers Bill Cordova Hinojosa %A Kim Pham %A Corinne Rouby %T Extension of the lubrication theory for arbitrary wall shape: An asymptotic analysis %J Comptes Rendus. Mécanique %D 2019 %P 389-396 %V 347 %N 5 %I Elsevier %R 10.1016/j.crme.2019.03.016 %G en %F CRMECA_2019__347_5_389_0
Rogers Bill Cordova Hinojosa; Kim Pham; Corinne Rouby. Extension of the lubrication theory for arbitrary wall shape: An asymptotic analysis. Comptes Rendus. Mécanique, Volume 347 (2019) no. 5, pp. 389-396. doi : 10.1016/j.crme.2019.03.016. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2019.03.016/
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