Two-dimensional flow of a non-Newtonian lubricant

The traction coefficients predicted in an elastohydrodynamic contact with a Newtonian fluid are impossibly large, so that methods of analysing the behaviour of a non-Newtonian fluid are essential. Except for one-dimensional flow, no convenient exact method is known. Two approximate methods of treating the flow of a non-Newtonian lubricant, proposed by Ehret et al. and Hooke respectively, are examined by comparing their predictions for a particular non-Newtonian fluid for which an exact solution may readily be obtained. While there is no reason to believe that any real fluid exhibits this behaviour, it is not too different from Eyring behaviour, so that the conclusions are believed to be applicable to real fluids. A method of obtaining an exact solution for a general non-Newtonian lubricant is investigated, although it appears to involve too much computation for use in an elastohydrodynamic lubrication (EHL) solver. A limited number of full solutions obtained for an Eyring fluid support the conclusions deduced using the model fluid, namely that the approximations will be quite adequate for the analysis of EHL of smooth surfaces and may be good enough for wavy or rough surfaces.