The Breakup of Liquid Volumes (how drops are formed)

The breakup of liquid volumes is a routinely observed phenomenon – e.g. when a jet of water emanating from a tap breaks up into droplets.  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. 

The challenge of capturing breakup, experimentally and computationally, is the strongly multiscale nature of this phenomenon.  Whilst the global dynamics may be on the scale of millimetres, as the breakup proceeds ever smaller length and time scales are encountered. Within the realm of continuum mechanics, which has been shown to retain accuracy right down to the nanoscale (Burton et al 04), one may have to capture 5-6 orders of magnitude in space and time.  This is completely intractable for CFD software.

Ideally, one could use computations down to a certain resolution and then rely on similarity solutions (relatively simple expressions which are accurate close to breakup) to finish the job.  However, to do so one  must establish the limits of applicability of these solutions, see Eggers & Villermaux 08, and this is what our recent article Capillary Breakup of a Liquid Bridge: Identifying Regimes & Transitions (accepted for publication in the Journal of Fluid Mechanics) has established for the first time.

To do so, 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 above.

The breakup event is, in the simplest case, characterised by an Ohnesorge number (a kind of dimensionless viscosity) whose value can have a dramatic effect on the dynamics.  For example, at intermediate Oh (video on left) the breakup occurs at two points so that a small drop is formed in the middle (a so-called 'satellite drop', which technologically is usually bad news) whereas at higher Oh (right) the breakup occurs in the centre.  Mapping our results across all Oh, tracking the minimum radius of breakup, we have been able to establish where similarity solutions are accurate and, as a by-product, have discovered a number of interesting previously undiscovered features of the breakup which deserve futher attention.

An obvious question to ask is what happens to the breakup when the thread reaches molecular scales?  The simple answer is, we don't know! Despite some progress in Moseler & Landman 00, there has been relatively little achieved in this direction.  Similarly, the 'reverse' process of coalescence has only recently received any attention  (e.g. in Pothier & Lewis 12).  This is somewhat surprising, as the related problem of dynamic wetting has received a huge amount of attention from the molecular dynamics community (e.g. DeConinck & Blake 08).  Consequently, a clear opportunity exists for us to exploit molecular simulation techniques to better understand breakup/coalescence phenomena at the nanoscale.