The breakup of liquid volumes is a process that is ubiquitous throughout industry and nature. Recently, this process has attracted significant attention due to its importance for the functioning of a range of microfluidic technologies where one would like to be able to control the generation of uniform sized droplets which then become building blocks, as in 3D printers, or modes of transport for reagents, as in lab-on-a-chip devices.

Computations of the Breakup

We have developed a finite element code which allows us to simultaneously resolve 4-5 orders of magnitude in space in order to capture the final stages of breakup. This has been achieved in the liquid bridge geometry shown below.

Typical simulation of the breakup of a liquid bridge trapped between stationary plates, showing the formation of a satellite drop.

Identifying Regimes and Transitions

Computations are used to establish the accuracy of various scaling laws, see [Eggers & Villermaux 08], proposed for the breakup to identify regimes and their transitions. To do so, one must map parameter space as characterised by the Ohnesorge number (a kind of dimensionless viscosity), whose effect on the breakup can be seen below.

Our article on this topic, entitled ``Capillary Breakup of a Liquid Bridge: Identifying Regimes and Transitions'', has been accepted for publication in the Journal of Fluid Mechanics, and a preprint can be obtained here.

Close-up of computations at Oh=0.001, 0.16, 10 (from left to right) showing differing dynamics of breakup. Notably, at the lowest Oh sharp corners are formed in the free surface whilst at the highest Oh no satellite drops are seen.

Open Problems

Our research has identified a number of challenges for future theoretical and computational research in this field. Perhaps most intriguingly, we have found that convergence towards the `universal' similarity solution of Eggers is oscillatory, as can be seen from the plot below of distance from breakup against breakup speed, in contrast to the Stokes flow solution of Papageorgiou, where the convergence is monotonic (curve 1 is for Oh=0.16 and curve 2 is for Oh=10). Identifying this phenomenon experimentally and gaining a deeper theoretical understanding of its origins remains an open problem.

Different Models

An alternative approach is to use a singularity free model, the interface formation model [Shikhmurzaev 05], and the initial results of this work can be found in the talks below.

Talks

Our research in this area was presented at the 2013 APS DFD meeting in Pittsburgh by Dr Yuan Li and the presentation can be found here [Li et al, 13]. A more recent talk by Dr Li, given at the BAMC 2014, is also available [Li, Oliver & Sprittles 14].