Flow factor of non‐continuum fluids in one‐dimensional contact
Authors: Zhang Y. 
Published: July 2006

Purpose

To develop a more realistic model for molecularly thin film hydrodynamic lubrication by incorporating the fluid inhomogeneity and discontinuity effects across the fluid film thickness in this lubrication.

Design/methodology/approach

The total mass flow of the fluid through the contact in a basic one‐dimensional molecularly thin film hydrodynamic lubrication is studied by incorporating the fluid inhomogeneity and discontinuity effects across the fluid film thickness, based on a simplified momentum transfer model between neighboring fluid molecules across the fluid film thickness. This flow is calculated according to the present approach and the theory of viscous flow between two contact surfaces. The total mass flow of the fluid through the contact in this lubrication is also calculated from conventional hydrodynamic lubrication theory, which was based on continuum fluid assumption in the whole lubricated contact. The ratio of this flow calculated from the present approach to that calculated from conventional hydrodynamic lubrication theory is here defined as the flow factor for a one‐dimensional molecularly thin film hydrodynamic lubrication due to the fluid inhomogeneity and discontinuity effects. Results of this flow factor are presented for wide operational parameters.

Findings

In the molecularly thin film hydrodynamic lubrication, when the fluid inhomogeneity and discontinuity across the fluid film thickness both are incorporated, the total fluid mass flow through the contact and thus the global fluid film thickness are increased. The combined effect of the fluid inhomogeneity and discontinuity across the fluid film thickness on the total fluid mass flow through the contact in this lubrication is determined by the operational parameter K=((∂p/∂xh2)/[6ηbulk(1−ξ)(ua+ub)]); when the operational parameter K is high, this effect is significant; when the operational parameter K is low, this effect is negligible. On the other hand, in this lubrication, when the combined effect of the fluid inhomogeneity and discontinuity across the fluid film thickness is incorporated, the shear stresses at the contact‐fluid interfaces are reduced and this reduction can be significant. This reduction may strongly depend on the value of the dimensionless discontinuity parameter Δ/D of the fluid across the fluid film thickness but weakly depend on the number n of the fluid molecules across the fluid film thickness.

Practical implications

An important and very useful research for the academic researcher and the engineer who are, respectively, engaged in the study and design of hydrodynamic lubrication on mechanical components especially of very low hydrodynamic lubrication film thickness. It is also important to the subsequent research of molecularly thin film hydrodynamic lubrication.

Originality/value

A new model of molecularly thin film hydrodynamic lubrication in one‐dimensional contacts is originally proposed and described by incorporating the fluid inhomogeneity and discontinuity effects across the fluid film thickness in this lubrication. This new model of molecularly thin film hydrodynamic lubrication is of importance to the theoretical study of molecularly thin film hydrodynamic lubrication.