Edge Contact Lubrication
Abstract
In this paper we discuss the dynamics of a lubricating film separating two flat surfaces. It may be possible for the gap between the surfaces to reduce to zero at one point on the boundary in a finite time. Typically, the maximum pressure diverges as the gap between the surfaces approaches zero. We discuss the form of the pressure field in the vicinity of its maximum. We also introduce a numerical method for accurate determination of the pressure across the lubrication surface, enabling us to determine the hydrodynamic forces. We determine the phase diagram describing the evolution of the gap, as a function of the initial configuration and of the line of action of the external forces. When contact does occur, we consider whether the subsequent motion involves sliding of the point of contact. We argue that, when sliding does occur, the motion does not depend upon the microscopic properties of the surface roughness.
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BibTeX
@misc{wilkinson2026edge,
title = {{Edge Contact Lubrication}},
author = {Andrew Wilkinson and Michael A. Morgan and Michael Wilkinson},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.24375},
eprint = {2609.24375},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.24375},
}
RIS
TY - UNPB
TI - Edge Contact Lubrication
AU - Andrew Wilkinson
AU - Michael A. Morgan
AU - Michael Wilkinson
PY - 2026
DA - 2026/09/21
PB - arXiv
DO - 10.48550/arxiv.2609.24375
UR - https://arxiv.org/abs/2609.24375
AB - In this paper we discuss the dynamics of a lubricating film separating two flat surfaces. It may be possible for the gap between the surfaces to reduce to zero at one point on the boundary in a finite time. Typically, the maximum pressure diverges as the gap between the surfaces approaches zero. We discuss the form of the pressure field in the vicinity of its maximum. We also introduce a numerical method for accurate determination of the pressure across the lubrication surface, enabling us to determine the hydrodynamic forces. We determine the phase diagram describing the evolution of the gap, as a function of the initial configuration and of the line of action of the external forces. When contact does occur, we consider whether the subsequent motion involves sliding of the point of contact. We argue that, when sliding does occur, the motion does not depend upon the microscopic properties of the surface roughness.
ER -