Scaling theory for hydrodynamic lubrication, with application to non-Newtonian lubricants

Scaling arguments are developed for the load balance in hydrodynamic lubrication, and applied to non-Newtonian lubricants with a shear-thinning rheology typical of a structured liquid. It is argued that the shear thinning regime may be mechanically unstable in lubrication flow, and 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 recent theories of shear thickening in non-Brownian particulate suspensions is indicated.