Viscoelastic thin film lubrication in finite width channels

Polymer enhanced lubricants exhibit elasticity, enabling them to stretch over long distances. In thin film lubrication, their relaxation time approaches the short residence time scales within the thin channel, the ratio referred to as the Deborah number (De), leading to the onset of viscoelasticity. The polymer’s elasticity generates finite streamwise normal stresses (zero for a Newtonian lubricant) that can potentially increase the film’s load bearing capability. Using reduced-order models, we observe in sliding contacts with infinite width (neglecting then all spanwise variation in pressure, velocity and stress) a noticeable increase in the load and change in the pressure distribution as De increases, owing to these finite normal stresses. Here, we consider thin lubricated channels, having a finite length-to-width or aspect ratio (a). Using the Oldroyd-B constitutive relation to model the viscoelastic stresses, we predict the pressure distribution along the contact and the maximum load carrying capacity of the film (F), varying the Deborah number and the aspect ratio. We find the same beneficial increase observed in the infinite-width case. Interestingly, F, that is zero for a Newtonian lubricant due to asymmetric pressure profile along the channel, varies strongly versus the aspect ratio for each Deborah number.