Premium
Multi‐linearity algorithm for wall slip in two‐dimensional gap flow
Author(s) -
Ma G. J.,
Wu C. W.,
Zhou P.
Publication year - 2006
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.1848
Subject(s) - slip (aerodynamics) , slip line field , mechanics , slip ratio , shear stress , materials science , slip factor , critical resolved shear stress , boundary value problem , finite element method , geometry , shear (geology) , shear rate , mathematics , physics , structural engineering , engineering , mathematical analysis , composite material , rheology , thermodynamics , impeller
Wall slip has been observed in a micro/nanometer gap during the past few years. It is difficult to make a mathematical analysis for the hydrodynamics of the fluid flowing in a gap with wall slip because the fluid velocity at the liquid–solid interface is not known a priori . This difficulty is met especially in a two‐dimensional slip flow due to the non‐linearity of the slip control equation. In the present paper we developed a multi‐linearity method to approach the non‐linear control equation of the two‐dimensional slip gap flow. We used an amended polygon to approximate the circle yield (slip) boundary of surface shear stress. The numerical solution does not need an iterative process and can simultaneously give rise to fluid pressure distribution, wall slip velocity and surface shear stress. We analysed the squeeze film flow between two parallel discs and the hydrodynamics of a finite slider gap with wall slip. Our numerical solutions show that wall slip is first developed in the large pressure gradient zone, where a high surface shear stress is easily generated, and then the slip zone is enlarged with the increase in the shear rate. Wall slip dramatically affects generation of the hydrodynamic pressure. Copyright © 2006 John Wiley & Sons, Ltd.