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Physics of Fluids / Volume 17 / Issue 9 / ARTICLES / Interfacial Flows

Phys. Fluids 17, 092101 (2005); doi:10.1063/1.1985467 (23 pages)

Soft lubrication: The elastohydrodynamics of nonconforming and conforming contacts

J. M. Skotheim and L. Mahadevan

Department of Applied Mathematics and Theoretical Physics, Centre for Mathematical Sciences, Cambridge CB3 0WA, United Kingdom and Division of Engineering and Applied Sciences, Harvard University, Pierce Hall, 29 Oxford Street, Cambridge, Massachusetts 02138

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(Received 13 December 2004; accepted 13 May 2005; published online 2 September 2005)

We study the lubrication of fluid-immersed soft interfaces and show that elastic deformation couples tangential and normal forces and thus generates lift. We consider materials that deform easily, due to either geometry (e.g., a shell) or constitutive properties (e.g., a gel or a rubber), so that the effects of pressure and temperature on the fluid properties may be neglected. Four different system geometries are considered: a rigid cylinder moving parallel to a soft layer coating a rigid substrate; a soft cylinder moving parallel to a rigid substrate; a cylindrical shell moving parallel to a rigid substrate; and finally a cylindrical conforming journal bearing coated with a thin soft layer. In addition, for the particular case of a soft layer coating a rigid substrate, we consider both elastic and poroelastic material responses. For all these cases, we find the same generic behavior: there is an optimal combination of geometric and material parameters that maximizes the dimensionless normal force as a function of the softness parameter η = hydrodynamic pressure/elastic stiffness = surface deflection/gap thickness, which characterizes the fluid-induced deformation of the interface. The corresponding cases for a spherical slider are treated using scaling concepts.

© 2005 American Institute of Physics

Article Outline

  1. INTRODUCTION
  2. FLUID LUBRICATION THEORY
  3. ELASTIC “LUBRICATION” THEORY: DEFORMATION OF A THIN ELASTIC LAYER
  4. DEGENERATE CONTACT
  5. SOFT SLIDER
  6. INCOMPRESSIBLE LAYER
  7. POROELASTIC LAYER
    1. Low speed: τm⪢τp
    2. High speed: τm⪡τp
    3. Intermediate speeds: τm ∼ τp
  8. ELASTIC SHELL
  9. JOURNAL BEARING
  10. THREE-DIMENSIONAL LUBRICATION FLOW
  11. DISCUSSION

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KEYWORDS and PACS

Keywords

porous materials, lubrication, elastodynamics, hydrodynamics, elastic deformation, machine bearings, elastic constants, flow through porous media

PACS

  • 47.85.Dh

    Hydrodynamics, hydraulics, hydrostatics

  • 47.56.+r

    Flows through porous media

  • 46.55.+d

    Tribology and mechanical contacts

  • 46.40.Jj

    Aeroelasticity and hydroelasticity

  • 46.25.-y

    Static elasticity

ARTICLE DATA

Permalink
http://link.aip.org/link/doi/10.1063/1.1985467

PUBLICATION DATA

ISSN:

1070-6631 (print)  
1089-7666 (online)

Publisher:

$abstract.society.value is a Member of CrossRef American Institute of Physics

For access to fully linked references, you need to log in.
    A. Martin, J. Clain, A. Buguin, and F. Brochard-Wyart, "Wetting transitions at soft, sliding interfaces," Phys. Rev. E 65, 031605 (2002).

    M. Abkarian, C. Lartigue, and A. Viallat, "Tank treading and unbinding of deformable vesicles in shear flow: Determination of the lift force," Phys. Rev. Lett. 88, 068103 (2002).

    M. A. Biot, "General theory of three-dimensional consolidation," J. Appl. Phys. 12, 155 (1941)JAPIAU000012000002000155000001.

    J. M. Skotheim and L. Mahadevan, "Soft lubrication," Phys. Rev. Lett. 92, 245509 (2004).


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