Line contact lubricated by a fluid described by non-Newtonian Giesekus model

Modelling hydrodynamic lubrication helps engineers and material scientists designing lubricants that minimize viscous energy losses without compromising the durability of engine components. This type of modelling requires selecting lubricant rheological constitutive equations that provide realistic information on fluid behaviour within tribological contact zones. Due to complexity of differential constitutive equations the modelling effort was limited to generalized Newtonian or Oldroyd-B fluids. In this paper, we present more realistic description of hydrodynamic lubrication using the Giesekus fluid capturing both viscous shear thinning and the development of elastic stresses at high Weissenberg numbers. The problem analysis is done using a modified regular perturbation method with respect to the small mobility parameter alpha. The perturbation analysis modification is caused by the fact that the problem contains several alpha priori unknown boundaries. The actual perturbation solutions for functions of pressure and gap, as well as the coordinate of exit from the contact and the exit film thickness, are obtained as linear functions of alpha. The effects of the model parameters such as the mobility factor, relaxation time and the polymer contribution to viscosity on pressure, shear and extensional viscosities within the contact zone are analysed. It is shown that the presence of polymers helps to increase the gap and reduce the viscous losses associated with hydrodynamic friction. This result is consistent with empirical observations of fuel economy enhancement for polymer-containing lubricants.