Analysis of the lubrication by a pseudoplastic fluid: Application to wire drawing

The analysis of the plane isothermal flow of a thin pseudoplastic film with the viscosity index m is performed. The Reynolds equation related to the Newtonian case (m=1) is changed in a system of two equations, one giving the location of the zero shear stress, the other the pressure gradient. This system is applied to the analysis of the lubrication of the wire drawing with a cylindrical nozzle. We obtain so an analytical expression of the pressure Δp generated by the nozzle and the flowing thickness h0. The approximate analysis based on the Reynolds equation overestimates Δp and h0.