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A continuum approach to reproduce molecular-scale slip behaviour

Published online by Cambridge University Press:  02 February 2010

H.-Y. HSU  and
N. A. PATANKAR
H.-Y. HSU
Affiliation:
Department of Mechanical Engineering, Northwestern University, 2145 Sheridan Road, Evanston, IL 60208-3111, USA
N. A. PATANKAR*
Affiliation:
Department of Mechanical Engineering, Northwestern University, 2145 Sheridan Road, Evanston, IL 60208-3111, USA
*
†Email address for correspondence: n-patankar@northwestern.edu
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Abstract

In this work we explore if it is possible to reproduce molecular-scale slip behaviour by using continuum equations. To that end it is noted that molecular-scale slip is affected by three factors: (i) near the wall, the fluid experiences a potential because of the wall; (ii) the fluid density responds to that potential, and hence, fluid compressibility is relevant; and (iii) the fluid can lose momentum to the wall. To incorporate these features we simulate shear flow of a compressible fluid between two walls in the presence of a potential. Compressibility effect is found to be important only in the near-wall region. The slip length is calculated from the mean velocity profile. The slip-length-versus-shear-rate trend is similar to that in molecular dynamic calculations. First, there is a constant value of the slip length at low shear rates. Then, the slip length increases beyond a critical shear rate. Lastly, the slip length reaches another constant value if the wall momentum loss parameter is non-zero. The scaling for the critical shear rate emerges from our results. The value of the slip length increases if the wall potential is less corrugated and if the momentum loss to the wall is low. An understanding of the overall force balance during various slip modes emerges from the governing equations.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 645 , 25 February 2010 , pp. 59 - 80
Copyright
Copyright © Cambridge University Press 2010

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