The role of viscoelastic stress in an abruptly converging/diverging channel under the thin film approximation

We analyze a viscoelastic fluid, modeled by the Oldroyd-B constitutive equation, flowing in a sliding abruptly converging/diverging channel. We have chosen this geometry since it has connections to the typical elastohydrodynamic lubricated (EHL), for which recently (Sarı et al., 2024) have illustrated how a viscoelastic lubricant has a positive effect on the tribological performance by raising load and decreasing friction coefficient. We assume that the channel is thin and the magnitude of the “jump” is small enough allowing to take advantage of the thin film approximation. We observe that the step location is a critical factor for generating viscoelastic pressure due to the positive and constant increase in the volumetric flow rate. Presence of viscoelasticity quantified by the ratio between fluid relaxation time and residence time, called Deborah number. A high Deborah number leads to a significant increment in pressure if the step is close to the inlet, while, if it is close to an outlet, the pressure decreases compared to Newtonian flows. While in most of the work, the pressure at the boundaries (inlet and outlet) is set to zero, we also tested more realistic boundary conditions in which the pressure is equal to the average elastic stress, showing that the two kinds of boundary conditions have a similar qualitative behavior. Lastly, a texture geometry, composed by one converging followed by one diverging steps, is inspected to mimic an EHL profile. We find what is the optimal distance between the steps to maximize the load. The role of the elastic stress in this texture profile is finally discussed.