Dripping to Jetting Transitions in Coflowing Liquid Streams

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"Dripping to Jetting Transitions in Coflowing Liquid Systems" Andrew S. Utada, Alberto Fernandez-Nieves, Howard A. Stone, and David A. Weitz Physical Review Letters 99, 094502 (2007)

Soft Matter Keywords

Droplet, jetting, dripping, surface tension, viscous shear, drop formation, microfluidics.

Overview

Refer to abstract of paper

Soft Matter Examples

When the flow rate of a kitchen tap increases slowly, drops initially grow and break off when the body force due to gravity acting on the drop overcomes the surface tension forces keeping the drop attached to the water in the tap. This is called "dripping". For viscous fluids, as the flow rate reaches a critical level, the liquid becomes a jet and drops at the tip of the jet break off when the inertial forces of the water overcomes the surface tension forces. For low viscosity fluids, the jets form Rayleigh-Plateau instability and break off. Anytime when a jet forms before breaking off into droplets, it is called "jetting".

When the same problem is applied to co-flowing liquid-liquid microfluidic devices, two different behaviors occur.

1. qout is larger than qin (Fig. 1a)

In this case, the viscous shear forces of the outer fluid are what drive the forming drop foward. At small qin and qout, dripping occurs (Fig. 1b) as the balance of surface tension and viscous shear force from the outside fluid dictates the size of the break-off drop. As qin/qout becomes smaller, a jet forms and the break off point departs from the nozzle of the inner fluid. The jet develops undulations driven by the Rayleigh-Plateau instability.

When dripping occurs, the size of the droplet can be estimated by a force balance between viscous shear force of the outside fluid and the surface tension of the inner fluid, <math>\mu_{out} u_{out} d_{out} \propto \gamma_{in} d_{tip}</math>. When jetting occurs, the drop diameter can be determined by finding out the volume conateined in one wavelength of hte Rayleigh-Plateau instability, <math> \pi d_{jet}^2 \lambda / 4</math>. This volume is approximately the same as the volume of the drop. So <math>d_{drop} \approx 2 d_{jet}<\math>.