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.Comment: 6 pages, 5 figures, RevTeX 4.

Flory-Huggins theory for the solubility of heterogeneously-modified polymers

Many water soluble polymers are chemically modified versions of insoluble base materials such as cellulose. A Flory-Huggins model is solved to determine the effects of heterogeneity in modification on the solubility of such polymers. It is found that heterogeneity leads to decreased solubility, with the effect increasing with increasing blockiness. In the limit of extreme blockiness, the nature of the phase coexistence crosses over to a polymer-polymer demixing transition. Some consequences are discussed for the synthesis of partially modified polymers, and the experimental characterisation of such systems.Comment: 4 pages, 2 figures, RevTeX 4.