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TECHNICAL PAPERS

Stokes Flow in Thin Films

[+] Author and Article Information
D. E. A. van Odyck, C. H. Venner

University of Twente, Faculty of Engineering Technology, Enschede, The Netherlands

J. Tribol 125(1), 121-134 (Dec 31, 2002) (14 pages) doi:10.1115/1.1506317 History: Received October 19, 2001; Revised June 26, 2002; Online December 31, 2002
Copyright © 2003 by ASME
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Figures

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Illustration of staggered grid cells and numbering and location of variables around a specific gridcell numbered as (i,j). Pressures are defined at cell centers (dot) such as the point (i,j), horizontal velocities at the center of vertical cell-faces (horizontal bar, locations i−1/2,j,i−1/2,j+1, etc.), vertical velocities at the center of horizontal cell faces (vertical bar, locations i,j−1/2,i,j+1/2). The equation of continuity is defined at pressure points, the x momentum equation at horizontal velocity points, and the y momentum equation at the vertical velocity points. The shaded region indicates the finite volume used the discretization of the x-momentum equation in the point i−1/2,j. If variables are needed at points of this volume at which they are not defined on the grid, e.g., pi−1/2,j+1/2 they are approximated by interpolation, see appendix B.
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(a) Pressure as function of x for z=0 and z=h(x); and (b) streamlines: both as function of x and z for ε=0.1,λs=0.4,as=0.2.
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Two types of recirculation for ε=0.01: (a) large amplitude induced recirculation as=0.9 and λs=0.06; and (b) short wavelength induced recirculation as=0.4 and λs=0.02.
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R̄ as function of as for (a) ε=0.1; (b) ε=0.01; and (c) ε=0.001
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Limit of R̄/R̄max if ε/λs=constant and ε→0, for as=0.1
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Pressure at the surface z=0 (left) and z=h(x) (right) for the Reynolds solution (prey), the Stokes solution (ps) and a first (p1) and second order (p2) perturbation solution for the case ε=0.01 and as=0.4 while λs=0.04 (top) and λs=0.02 (bottom)
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The value of R̄ for the Stokes (S) solution, the first order perturbation (p1) solution and the second order perturbation (p2) solution for the SLF with ε=0.01 and λs=0.04
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(a) Pressure as function of x for z=0 and z=h(x); and (b) streamlines: both as function of x and z for ε=0.1,hloc=0.1,λs=0.04,as=0.08.
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The value of R̄ as function of as for different λs: (a) ε=0.1 and hloc=0.1; (b) ε=0.1 and hloc=0.01; and (c) ε=0.01 and hloc=0.1.
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Pressure at the surface z=0 (left) and z=h(x) (right) for the Reynolds solution (prey), the Stokes solution (ps) and a first-(p1) and second order (p2) perturbation solution for the case λs=0.04 (top) and λs=0.018 (bottom) while for both cases ε=0.1,hloc=0.1, and as=0.08
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The value of R̄ for the EHL geometry with local feature obtained for the case of the Stokes (S) solution the first order perturbation solution (p1) and the second order perturbation solution (p2).ε=0.1,hloc=0.1 and λs=0.04.
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Geometry for single local feature

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