Viscoplastic lubrication theory with application to bearings and the washboard instability of a planing plate

Journal of Non-Newtonian Fluid Mechanics

Volumn 169-170, Issue , 2012, Pages 74-90

  Hewitt, I J ^a   Balmforth, N J ^a  

^a UNIVERSITY OF BRITISH COLUMBIA   (Canada)

Author keywords

Instability; Lubrication; Viscoplastic; Yield stress

Indexed keywords

BINGHAM FLUID; FLUID FLUXES; FLUID LAYER; HERSCHEL-BULKLEY; IMPOSED LOADS; INCLINED PLATE; INNER CYLINDER; LIFT FORCE; LUBRICATION THEORY; MOVING BOUNDARIES; RHEOLOGICAL MODELS; SLIDER BEARINGS; VERTICAL OSCILLATIONS; VISCOPLASTIC; VISCOPLASTIC FLUID;

FLUIDS; JOURNAL BEARINGS; LUBRICATION; PLASMA STABILITY;

YIELD STRESS;

EID: 84856086383     PISSN: 03770257     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jnnfm.2011.11.008     Document Type: Article

References (39)

1. Pinkus O., Sternlicht B. Theory of Hydrodynamic Lubrication 1961, McGraw-Hill, New York.
2. Dowson D. Elastohydrodynamic and Micro-elastohydrodynamic lubrication. Wear 1995, 190:125-138.
3. Milne A.A. A theory of rheodynamic lubrication. Colloid Polym. Sci. 1954, 139:96-101.
4. Tichy J.A. Hydrodynamic lubrication theory for the Bingham plastic flow model. J. Rheol. 1991, 35:477-506.
5. Moyers-Gonzalez M., Frigaard I.A., Nouar C. Stable two-layer flows at all Re; visco-plastic lubrication of shear-thinning and viscoelastic fluids. J. non-Newt. Fluid Mech. 2010, 165:1578-1587.
6. Vajravelu K., Sreenadh S., Ramesh Babu V. Peristaltic transport of a Herschel-Bulkley fluid in an inclined tube. Int. J. Nonlinear Mech. 2005, 40(1):83-90.
7. D. Takagi, Nonlinear peristaltic waves, in: Proceedings of the Geophysical Fluid Dynamics Summer Study Program, Woods Hole Oceanopgraphic Institution, WHOI-2010-01, 2010.
8. Balmforth N.J., Coombs D., Pachman S. Microelastohydrodynamics of swimming organisms near solid boundaries in complex fluids. Quart. J. Mech. Appl. Math. 2010, 63:267-294.
9. Denny M.W. The role of gastropod mucus in locomotion. Nature 1980, 285:160-161.
10. Chan D., Balmforth N.J., Hosoi A. Building a better snail: lubrication theory and adhesive locomotion. Phys. Fluids 2005, 17:113101.
11. Walton I.C., Bittleston S.H. The axial flow of a Bingham plastic in a narrow eccentric annulus. J. Fluid Mech. 1991, 222:39-60.
12. Balmforth N.J., Craster R.V. A consistent thin-layer theory for Bingham fluids. J. Non-Newt. Fluid Mech. 1999, 84:65-81.
13. Batra R.L. Rheodynamic lubrication of a journal bearing. Appl. Sci. Res. A 1966, 15:331-344.
14. Liu K.F., Mei C.C. Slow spreading of Bingham fluid on an inclined plane. J. Fluid Mech. 1989, 207:505-529.
15. S. Pegler, Snail locomotion, in: Proceedings of the Geophysical Fluid Dynamics Summer Study Program, Woods Hole Oceanopgraphic Institution, WHOI-2011-01, 2010.
16. I.J. Hewitt, N.J. Balmforth, J.N. McElwaine, Granular and fluid washboards. J. Fluid Mech. (in press).
17. Beris A., Tsamopoulos J., Brown R.A., Armstrong R.C. Creeping motion of a sphere through a Bingham plastic. J. Fluid Mech. 1985, 158:219-244.
18. Putz A., Frigaard I.A. Creeping flow around particles in a Bingham fluid. J. Non-Newt. Fluid Mech. 2010, 165:263-280.
19. Brenner H. The slow motion of a sphere through a viscous fluid towards a plane surface. Chem. Eng. Sci. 1961, 16:242.
20. Mather K.B. Why do roads corrugate?. Scientific American 1963, 208:128-136.
21. Taberlet N., Morris S.W., McElwaine J.N. Washboard road: the dynamics of granular ripples formed by rolling wheels. Phys. Rev. Lett. 2007, 99.
22. Bitbol A., Taberlet N., Morris S.W., McElwaine J.N. Scaling and dynamics of washboard roads. Phys. Rev. E 2009, 79:79.061308.
23. Ruschak K.J. Coating flows. Ann. Rev. Fluid Mech. 1985, 17:65-89.
24. Witelski T.P. Dynamics of air bearing sliders. Phys. Fluids 1998, 10:698-708.
25. Saita F.A. Simplified models of flexible blade coating. Chem. Eng. Sci. 1989, 44:817-825.
26. Balmforth N.J., Craster R.V., Rust A.C., Sassi R. Viscoplastic flow over an inclined surface. J. Non-Newt. Fluid Mech. 2006, 139:103-127.
27. Wada S., Hayashi H., Haga K. Behavior of a Bingham solid in hydrodynamic lubrication (Part 1. General theory). Bull. Jpn. Soc. Mech. Eng. 1973, 16:422-431.
28. Matson G.P., Hogg A.J. Two-dimensional dambreak flows of Herschel-Bulkley fluids: the approach to the arrested state. J. Non-Newton. Fluid Mech. 2007, 142:79-94.
29. Huilgol R., Mena B., Piau J.M. Finite stopping time problems and rheometry of Bingham fluids. J. Non-Newton. Fluid Mech. 2002, 102:97-107.
30. Dorier C., Tichy J. Behaviour of a Bingham-like viscous fluid in lubrication flows. J. Non-Newton. Fluid Mech. 1992, 45:291-310.
31. Greener Y., Middleman S. Blade-coating of a viscoelastic fluid. Polym. Eng. Sci. 1974, 14:791-796.
32. Ross A.B., Wilson S.K., Duffy B.R. Thin-film flow of a viscoplastic material round a large horizontal stationary or rotating cylinder. J. Fluid Mech. 2001, 430:309-333.
33. Ewoldt R.H., Tourkine P., McKinley G.H., Hosoi A.E. Controllable adhesion using field-activated fluids. Phys. Fluids 2011, 23:073104.
34. Taylor G.I. Cavitation of a viscous fluid in narrow passages. J. Fluid Mech. 1963, 16:595-619.
35. Savage M.D. Mathematical models for coating processes. J. Fluid Mech. 1982, 117:443-455.
36. Pearson J.R.A. The stability of uniform viscous flow under rollers and spreaders. J. Fluid Mech. 1960, 7:481-500.
37. Tuck E.O., Schwartz L.W. A numerical and asymptotic study of some third-order ordinary differential equations relevant to draining and coating flows. SIAM Rev. 1990, 32:453-469.
38. Moriarty J.A., Terrill E.L. Mathematical modelling of the motion of hard contact lenses. Euro. J. Appl. Math. 1996, 7:575-594.
39. Quintans Carou J., Wilson S.K., Mottram N.J., Duffy B.R. Asymptotic and numerical analysis of a simple model for blade coating. J. Eng. Math. 2009, 63:155-176.