Tribology Letters

, Volume 41, Issue 3, pp 573–586

Modeling Bearing and Shear Forces in Molecularly Thin Lubricants

  • Antonis I. Vakis
  • Melih Eriten
  • Andreas A. Polycarpou
Original Paper

Abstract

Under the effects of high shear rate and confinement between solid surfaces, the behavior of a thin lubricant film deviates from that of the bulk, resulting in significant increases of lubricant viscosity and interfacial slip. A semi-empirical model accounting for the breakdown of continuum theory at the nanoscale is proposed—based on film morphology and chemistry from available experimental and molecular dynamics simulation data—to describe lubricant behavior under shear. Viscosity stiffening and interfacial slip models are introduced into the formulations of the normal (bearing) and shear forces acting on a sphere that moves within a thin lubricant film parallel to a rigid plane. The experimentally measured ‘apparent’ viscosity confounding the effects of both stiffening and slip is used to predict the hydrodynamic forces acting on a fully or partially submerged sphere for the purposes of describing lubricant contact in magnetic storage. The proposed sphere-on-flat model forms the basis of a future, dynamic contact with friction model that will account for lubricant contact in the context of molecularly thin lubricated rough surface contact.

Keywords

Nanotribology Magnetic data storage Sub-boundary lubrication Non-Newtonian hydrodynamic effects Viscoelasticity Rheology 

List of Symbols

A

Oscillation amplitude

a, b

Viscosity-gap model coefficients

a′, b

Viscosity-shear rate model coefficients

C

Molecular coverage of surface area

c

Damping coefficient (for fluid ‘contact’)

d0

Liquid gap

f

Driving frequency of oscillation

f*

Dimensionless slip factor

G

Storage modulus

G

Loss modulus

G*

Complex modulus

H

Heaviside function

h

Film thickness

hB

Average molecular height of bonded layer

h0

Solid-solid gap (minimum film thickness)

Ls

Slip length

p

Pressure

Pfluid

Normal (bearing) hydrodynamic force

Psolid

Normal solid force

Ptrans

Normal transitional force

Qfluid

Shear hydrodynamic force

Qsolid

Solid friction force

Qtrans

Shear transitional force

R

Sphere (probe or asperity) radius

S

Spherical cap area

t

Total lubricant layer thickness

U

Shearing velocity

u

Fluid velocity along x-direction

u*

Dimensionless form of u

us

Slip velocity

\( u_{\text{s}}^{*} \)

Dimensionless form of us

uw

Wall velocity (as boundary condition)

v

Fluid velocity in y-direction

v*

Dimensionless form of v

\( \dot{\gamma } \)

‘Apparent’ shear rate

\( \dot{\gamma }_{\text{true}} \)

‘True’ shear rate (accounting for slip)

ζ

Normalized y-coordinate

η

‘Apparent’ viscosity

ηtrue

‘True’ viscosity (decoupled from slip)

ηw

Wall friction (liquid–solid coupling)

η0

Maximum limiting viscosity

η

Bulk viscosity

η′

Viscosity (η = η′)

η″

Elasticity

η*

Complex viscosity

κ

Minimum liquid gap

λ

Normalized z-coordinate

ξ

Normalized x-coordinate

σ

Root-mean-square roughness of substrate

τ

Shear stress on sphere surface

Ω

Geometric factor

Ωf-s

Geom. f. for fully submerged sphere

Ωp-s

Geom. f. for partially submerged sphere

ω

Solid interference

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Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  • Antonis I. Vakis
    • 1
  • Melih Eriten
    • 1
  • Andreas A. Polycarpou
    • 1
  1. 1.Department of Mechanical Science and EngineeringUniversity of Illinois at Urbana-ChampaignUrbanaUSA

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