Capillary breakup of a liquid bridge: identifying regimes and transitions

Abstract

Computations of the breakup of a liquid bridge are used to establish the limits of applicability of similarity solutions derived for different breakup regimes. These regimes are based on particular viscous–inertial balances, that is, different limits of the Ohnesorge number $Oh$. To accurately establish the transitions between regimes, the minimum bridge radius is resolved through four orders of magnitude using a purpose-built multiscale finite element method. This allows us to construct a quantitative phase diagram for the breakup phenomenon which includes the appearance of a recently discovered low-$Oh$ viscous regime. The method used to quantify the accuracy of the similarity solutions allows us to identify a number of previously unobserved features of the breakup, most notably an oscillatory convergence towards the viscous–inertial similarity solution. Finally, we discuss how the new findings open up a number of challenges for both theoretical and experimental analysis.