Extension of the lubrication theory for arbitrary wall shape: An asymptotic analysis

Rogers Bill Cordova Hinojosa; Kim Pham; Corinne Rouby

doi:10.1016/j.crme.2019.03.016

Extension of the lubrication theory for arbitrary wall shape: An asymptotic analysis

Rogers Bill Cordova Hinojosa ¹; Kim Pham ¹ ; Corinne Rouby ¹

¹ IMSIA, CNRS, ENSTA ParisTech, 828, bd des Maréchaux, 91732 Palaiseau, France

Comptes Rendus. Mécanique, Volume 347 (2019) no. 5, pp. 389-396.

Abstract

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.

Received: 2019-01-23
Accepted: 2019-03-27
Published online: 2019-04-19

DOI: 10.1016/j.crme.2019.03.016

Keywords: Lubrication approximation, Stokes flow, Asymptotic expansions

Author's affiliations:

Rogers Bill Cordova Hinojosa ¹; Kim Pham ¹; Corinne Rouby ¹

¹ IMSIA, CNRS, ENSTA ParisTech, 828, bd des Maréchaux, 91732 Palaiseau, France

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     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},
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     volume = {347},
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     year = {2019},
     doi = {10.1016/j.crme.2019.03.016},
     language = {en},
}

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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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