Phase-field simulations for dripping-to-jetting transitions: Effects of low interfacial tension and bulk diffusion

The dripping-to-jetting transitions in coaxial flows have been experimentally well studied for systems of high interfacial tension, where the capillary number of the outer fluid and the Weber number of the inner fluid are in control. Recent experiments have shown that in systems of low interfacial tension, the transitions driven by the inner flow are no longer dominated by the inertial force alone, and the viscous drag force due to the inner flow is also quantitatively important. In the present work, we carry out numerical simulations based on the Cahn-Hilliard-Navier-Stokes model, aiming for a more complete and quantitative study that is needed for understanding the effects of interfacial tension when it becomes sufficiently low. The Cahn-Hilliard-Navier-Stokes model is solved by using an accurate and efficient spectral method in a cylindrical domain with axisymmetry, and numerical results obtained for jet and drop radii demonstrate the accuracy of our computation. Plenty of numerical examples are systematically presented to show the dripping-to-jetting transitions driven by the outer flow and inner flow respectively. In particular, for transitions dominated by inner flow, detailed results reveal how the magnitude of interfacial tension quantitatively determines the relative importance of the inertial and viscous forces due to the inner flow at the transition point. Our numerical results are found to be consistent with the experimental observation. Finally, the degree of bulk diffusion is varied to investigate its quantitative effect on the condition for the occurrence of transition. Such effect is expected for systems of ultralow interfacial tension where interfacial motion is more likely to be driven by bulk diffusion.