Tribology Letters

, Volume 49, Issue 1, pp 227–238 | Cite as

An Advanced Rough Surface Continuum-Based Contact and Sliding Model in the Presence of Molecularly Thin Lubricant

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


A model of molecularly thin lubricant layer behavior for rough, sliding contact is presented in this work as a function of lubricant layer morphology. Building on previous work by the authors where the lubricant layer was assumed to be uniform in thickness and morphology, lubricant contributions to contact are presently treated at the asperity level and the effects of lubricant bonding ratio and coverage are accounted for. Effective stiffnesses for lubricated asperities are used to calculate the bearing and shear forces, while variable surface energy is modeled at the asperity level and used within an improved continuum adhesive formulation. Contributions from asperities in lubricant and solid contact for partial coverage are determined within the context of a statistical mechanics model. The proposed model can be used to study the mixed nanolubrication regime expected during light contact or “surfing” recording in magnetic storage, where sustained nanolubricant contact would partially deplete mobile molecules from the contact interface.


Nanotribology Magnetic data storage Roughness effects Adhesion Boundary lubrication friction 

List of Symbols


Nominal area of contact


Bonding ratio


Coverage ratio


Surface energy fitting coefficients


Mean plane separation (asperity heights)


Liquid gap = h 0 − κ

E, E1,2

Young’s modulus of solid substrates


Total adhesive force


Adhesive force in lubricant


Non-contact adhesive force




Mean plane separation (surface heights)


Solid–solid gap


Maximum contact pressure factor


Solid contact stiffness


Solid frictional stiffness


Total lateral (frictional) stiffness


Total normal (contact) stiffness


Bearing (normal) stiffness


Shear stiffness


Spectral moments


Bearing force curve-fitting coefficient


Number of asperities


Shear force curve-fitting coefficient


Total contact force


Maximum experimental bearing force


Bearing force


Total frictional force


Maximum experimental shear force


Lubricant shear force

R, R1,2

Mean radius of asperity


Logistic function switch


Total average lubricant thickness


Mobile lubricant thickness


Shearing (sliding) velocity


Lateral direction (along slider motion)


Asperity height

\( \dot{\gamma } \)

Shear rate


Surface free energy


Equilibrium spacing

η, η1,2

Areal density of asperities


Minimum liquid gap


Coverage cutoff distance factor

ν, ν1,2

Poisson ratio


Disjoining pressure

σ, σ1,2

RMS roughness of asperity heights


RMS roughness of surface heights


Gaussian distribution PDF


PDF of lubricant-contacting asperities


PDF of non-contacting asperities


Interference = zdε


Critical interference



This study falls under the Cyprus Research Promotion Foundation’s Framework Programme for Research, Technological Development and Innovation 2009–2010 (DESMI 2009–2010), cofunded by the Republic of Cyprus and the European Regional Development Fund, and specifically under Grant PENEK/0609/03.


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Copyright information

© Springer Science+Business Media New York 2012

Authors and Affiliations

  1. 1.Department of Electrical and Computer EngineeringUniversity of CyprusNicosiaCyprus
  2. 2.Department of Mechanical Science and EngineeringUniversity of Illinois at Urbana-ChampaignUrbanaUSA
  3. 3.Department of Mechanical EngineeringKhalifa University of Science Technology and ResearchAbu DhabiUAE

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