(315c) Confined Droplets At T-Junctions

We analyze droplet breakup in confined T-junction geometries. The aims of this talk are to elucidate the break-up mechanism, to use this understanding to predict whether a droplet will break up or drift away to one of the branches, and to describe behavior close to the critical transition from breaking to drifting. 

Earlier work (Link et al., 2004) had pointed to a breakup mechanism akin to Rayleigh-Plateau instability, whereas Leshansky and coworkers found (2009, 2012) that experimental data could equally well be explained without any capillary instability using a two-dimensional steady-state analysis. We show that a capillary instability is crucial in the description of the final stages of collapse. This instability is compared to end-pinching and to Rayleigh-Plateau instability found in unconfined droplets. Only for the early stages of breakup, three-dimensional effects are not important. Predicting when the droplet breaks needs the full 3D analysis.

Whether a droplet breaks is an unresolved fundamental problem. All experimental data to date indicate that there is a certain droplet length, beyond which all droplets will always break, whatever the flow speed. We present careful experiments that show that this is not the case, with long droplets that do not break at sufficiently small flow speeds. It may take a long time to drift away to one side (> 30 minutes in some experiments), but drift away they do. This experimental phase diagram that spans many decades of the capillary number allows the further development of theory.

Many practical applications will want to operate with rather short droplets at rather slow speeds, i.e. close the the critical line that marks the transition from drifting to breaking. We analyze how close to this transition, the timescale for drifting and the timescale for breakup become comparable, leading to a good description of the asymmetric breakup that occurs under these conditions.

This work provides insight into the behavior of confined droplets and predicts traffic of droplets in microfluidic networks for lab-on-a-chip applications.

D.R. Link et al, PRL 2004

Leshansky and Pismen, Phys. Fluids, 2009

Leshansky and Pismen, PRL, 2012

Hoang et al, Journal of Fluid Mechanics, 2013