# Difference between revisions of "Monodisperse double emulsions generated with a microcapillary device"

Original entry by A.J. Kumar, APPHY 225 Fall 2009

## Reference

A.S. Utada, E. Lorenceau, D.R. Link, P. Kaplan, H.A. Stone and D.A. Weitz , Science 308, 537-541, 2005.

## Keywords

Double emulsion, Microcapillary, microfluidics, emulsion

## Summary

In this paper, the authors present a mechanism by which to produce monodisperse double emulsions with a high degree of control. Previously, methods to produce double emulsions resulted in a high degree of variability, making overall yield of useful double emulsions quite small. A double emulsion requires three fluids, the suspension liquid, the middle liquid, and the inner liquid. The authors method involves using microfluidics and a microcapillary device pictured in Figure 1.

They then stream in the three desired fluids around the microcapillary and are able to control the formation of emulsions using different geometries and flow rates. The resulting emulsions display a high degree of uniformity. The authors observe two primary mechanisms by which the droplets are pinched off which they call the "drip" and "jet" mechanisms. The transition comes from finding the relevant timescales. For a cylindrical liquid jet, the pinch off is governed by the Rayleigh-Plateau instability and grows with a characteristic time. However, the Rayleigh-Plateau instability can only form after the the length of the jet has grown to the length of it's radius, giving a second time parameter. The ratio of these gives an effective capillary number below which "drip" behavior dominates and above which "jet" behavior dominates.

In the drip regime, the flow rate of the suspension liquid is low and surface forces dominate. They create a theoretical model that relates the mass flux to the cross-sectional area and derive the following relations:

$\frac{Q_{sum}}{Q_{OF}} = \frac{\pi R_{jet}^2}{\pi R_{orifice}^2-\pi R_{jet}^2}$ [1]

Where $Q_{sum}$ is the summative flow rate of the inner liquids, $Q_{OF}$ is the flow rate of the outer, suspension fluid and the R's refer the the relevant radiuses.

In the jet regime. The Rayleigh-Plateau instability dominates and leads to the relation:

$R_{drop} = (\frac{15 Q_{sum} R_{jet} \eta_{OF}}{\pi \gamma})$ [2]

The authors predict the behavior will shift between these regimes when their defined capillary number is near one. They find good agreement between their theory and experimental data as shown in Figure 2.

In conclusion, not only do the authors present an extremely useful new technique but they also match it with a reasonable theory which allows tunability to produce emulsion droplets with different radii and contents.

in progress ...