Sliding friction in the hydrodynamic lubrication regime for a power-law fluid

TL;DR

This paper presents a scaling analysis of sliding friction in hydrodynamic lubrication for shear-thinning fluids, revealing potential discontinuities and hysteresis in the friction behavior due to mechanical instability when the fluid's shear-thinning is significant.

Contribution

It introduces a theoretical framework analyzing the stability of shear-thinning fluids in lubrication, highlighting conditions leading to discontinuous friction curves and potential hysteresis effects.

Findings

Shear-thinning fluids with n<1/2 are mechanically unstable in lubrication.

The Stribeck curve may exhibit discontinuities and hysteresis due to instability.

Normal stresses and flow transients do not fundamentally alter the instability picture.

Abstract

A scaling analysis is undertaken for the load balance in sliding friction in the hydrodynamic lubrication regime, with a particular emphasis on power-law shear-thinning typical of a structured liquid. It is argued that the shear-thinning regime is mechanically unstable if the power-law index n < 1/2, where n is the exponent that relates the shear stress to the shear rate. Consequently the Stribeck (friction) curve should be discontinuous, with possible hysteresis. Further analysis suggests that normal stress and flow transience (stress overshoot) do not destroy this basic picture, although they may provide stabilising mechanisms at higher shear rates. Extensional viscosity is also expected to be insignificant unless the Trouton ratio is large. A possible application to shear thickening in non-Brownian particulate suspensions is indicated.