The spread of a viscoelastic circular jet and hydraulic jump

We examine theoretically the spread of a jet impacting on a circular disk and the hydraulic jump of a viscoelastic fluid of the Oldroyd-B type. The depth-averaging approach is employed in the supercritical region. The subcritical flow is assumed to be inertialess of the lubrication type, and the downstream boundary condition is assumed to be a known parameter. The jump is treated as an abrupt shock, where the balance of mass and momentum is applied across it in the radial direction. The influence of viscoelasticity on the flow behavior is deduced by comparing against the well-established Newtonian limit. The analysis of the flow in the thin-film region reveals that the film thickness increases with viscoelasticity, aligning with the findings of previous studies on viscoelastic thin-film flows. Overall, all elastic stresses diminish downstream of the jump, implying that the contribution of viscoelasticity in the formation of the jump can be predominantly attributed to the rise of the elastic stresses upstream. It is found that viscoelasticity yields an increase in the jump height and a decrease in its radius, resulting in the jump occurring in closer proximity to the impingement point. A dimensionless group involving Deborah number and solute-to-polymer viscosity ratio successfully collapses the predicted jump radius onto a single curve, suggesting the configuration's potential as a rheometer. At high Deborah numbers, the jump radius remains unchanged with varying downstream conditions. As gravity decreases, a small hump in the film manifests in the upstream region, and the jump radius becomes larger.