Steady and Unsteady Buckling of Viscous Capillary Jets and Liquid Bridges

Steady buckling (coiling) of thin falling liquid jets is sensitive to surface tension, yet an understanding of these capillary effects lags far behind what is known about surface-tension-free coiling. In experiments with submillimetric jets and ultralow flow rates, we find that the critical dispensing height H_{c} for coiling decreases with increasing flow rate, a trend opposite to that found previously for inertia-free coiling. We resolve the apparent contradiction using nonlinear numerical simulations based on slender-jet theory which show that the trend reversal is due to the strong effect of surface tension in our experiments. We use our experiments to construct a regime diagram (coiling vs stagnation flow) in the space of capillary number Ca and jet slenderness ε and find that it agrees well with fully nonlinear numerical simulations. However, it differs substantially from the analogous regime diagram determined experimentally by Le Merrer, Quéré, and Clanet [Phys. Rev. Lett. 109, 064502 (2012)PRLTAO0031-900710.1103/PhysRevLett.109.064502] for the unsteady buckling of a compressed liquid bridge. Using linear stability analysis, we show that the differences between the two regime diagrams can be explained by a combination of shape nonuniformity and the influence of gravity.