Dripping, Jetting, Drops, and Wetting: The Magic of Microfluidics

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Original entry: Zach Wissner-Gross, APPHY 226, Spring 2009

Information

Dripping, Jetting, Drops, and Wetting: The Magic of Microfluidics

A. S. Utada, L.-Y. Chu, A. Fernandez-Nieves, D. R. Link, C. Holtze, and D. A. Weitz

MRS Bulletin, 2007, 32, 702-708

Soft matter keywords

Surface tension, Rayleigh-Plateau instability, hydrodynamic focusing, emulsion, capillary number, Weber number

Summary

Figure 1: Co-flow capillaries for droplet production.
Figure 2: Flow-focusing capillaries for droplet production.
Figure 3: Cascading co-flow capillaries resulting in both jetting and dripping behavior. Scale bar is <math>200 \mu</math>m.
Figure 4: Triple emulsions. Scale bars are <math>200 \mu</math>m.

David Weitz and coworkers describe their work creating emulsions using precisely aligned concentric capillary tubes. They introduce two geometries for making these controlled emulsions: with coaxial flow, an outer fluid flow provides a shear force that pulls droplets out from an inner capillary (Figure 1), whereas with flow-focusing, the flow of the outer fluid (rather than the tube itself) focuses the inner fluid before shearing, producing noticeably smaller droplets (Figure 2).

The authors go on to realize that with coaxial flow, or co-flow as they call it for short, they can create cascading emulsion events with relative ease and control (Figure 3). Most impressive is the authors' "monodisperse triple emulsions," that make use of such recursion (Figure 4). By changing relative flow rates, they can alter the number of drops at each level in the hierarchy.

Finally, the authors run through an impressive list of applications for their technology. Using diblock copolymers as a surfactant and by evaporating intermediate droplets among a series of concentric droplets, they can create "polymerosome structures," such as lipid bilayers, or even bilayers with different polymers inside and outside (so-called "asymmetric polymerosomes"), which resemble the intra- and extracellular surfaces of cell membranes. Weitz and coworkers have created shells of liquid crystals and polymerizable hydrogels, and have even seeded triple emulsion droplets in thermosensitive gels, which shrink at higher temperatures, thereby tearing intermediate layers of the droplets for controlled release of the inner layers (think drug delivery!).

Soft matter discussion

The notable soft matter physics discussion in the article occurs when the authors study the transition between the dripping of droplets from capillaries and fluid "jetting" out of the capillaries. Due to the Rayleigh-Plateau instability, jets will always decay into more stable drops, but there is an observable transition between what emerges from the inner capillary in Figure 1: it can be jets that later decay into drops, or it can be drops that depart from the capillary, without any jets (see Figure 3).

This dripping-to-jetting transition at the capillary tip depends on two physical constants: the Weber number and the capillary number, both of which can be thought of as dimensionless force ratios. The capillary number is the ratio of stress forces induced by the surrounding outer fluid (Figure 1) to the surface tension forces of the fluid interface. The Weber number is the ratio of inertial forces within the inner fluid to the surface tension forces.

Figure 5: Dependence of dripping/jetting behavior on capillary number of the outer fluid and Weber number of the inner fluid for co-flow devices. Filled symbols indicate jetting behavior, while unfilled symbols indicate dripping behavior.

When the Weber number is large (i.e., We >> 1), the inner fluid is quickly swelling up to form a drop and instabilities lead to the drop pinching off as it leaves the inner capillary. When the capillary number is large (i.e. Ca >> 1), the shear stresses on the drop are then sufficient to pinch it off before a jet can form. In Figure 5, the authors show experimental data that clearly marks the transition between dripping and jetting when We + Ca is of order 1.