Finite element solution of viscous jet flows with surface tension

A finite element method is used to study the effect of Reynolds number and surface tension on the expansion and contraction of jets of Newtonian liquids. For values of Reynolds numbers (based on tube diameter), below 14 the jets expand, and when Re > 14 the jets contract. For higher Reynolds numbers the jet diameter approaches a limiting value. It is also found that the surface tension has a considerable effect on low Reynolds number jet flows, becoming negligible at higher Reynolds numbers. As an example, if the surface tension parameter $\text{σ}\text{η}\text{u}$ is equal to unity, the creeping flow jet expansion is reduced by 4% relative to the case with no surface tension but when Re is equal to 20 and 50 the final jet diameters increase by only 0.2%. The calculated jet shapes are compared with available experimental results.