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
, Kim Pham
, Corinne Rouby

ENSTA-ParisTech

Research output: Contribution to journal › Article › peer-review

8 Citations (Scopus)

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.

Original language	English
Pages (from-to)	389-396
Number of pages	8
Journal	Comptes Rendus - Mecanique
Volume	347
Issue number	5
DOIs	https://doi.org/10.1016/j.crme.2019.03.016
Publication status	Published - 1 May 2019

Keywords

Asymptotic expansions
Lubrication approximation
Stokes flow

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10.1016/j.crme.2019.03.016

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title = "Extension of the lubrication theory for arbitrary wall shape: An asymptotic analysis",

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.",

keywords = "Asymptotic expansions, Lubrication approximation, Stokes flow",

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T2 - An asymptotic analysis

AU - Hinojosa, Rogers Bill Cordova

AU - Pham, Kim

AU - Rouby, Corinne

PY - 2019/5/1

Y1 - 2019/5/1

N2 - 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.

AB - 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.

KW - Asymptotic expansions

KW - Lubrication approximation

KW - Stokes flow

U2 - 10.1016/j.crme.2019.03.016

DO - 10.1016/j.crme.2019.03.016

M3 - Article

AN - SCOPUS:85064407747

SN - 1631-0721

VL - 347

SP - 389

EP - 396

JO - Comptes Rendus - Mecanique

JF - Comptes Rendus - Mecanique

IS - 5

ER -

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

Abstract

Keywords

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