Dripping to Jetting Transitions

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Original entry by Hyerim Hwang, AP 226, Spring 2012.

Reference

Andrew S. Utada, Alberto Fernandez-Nieves, Howard A. Stone, and David A. Weitz, "Dripping to Jetting Transition in Coflowing Liquid Streams", Physics Review Letters 2007 99, 094502

Keywords

Jetting, Dripping, Surface Tension, Microfluidics, Droplet

Introduction

Figure 1. (a) Device geometry showing the tapered inner capillary in the outer square capillary. (b) Dripping regime. (c) Narrowing jet. (d) Widening jet.

A liquid forced through an orifice will ultimately break into drops due to surface tension. Drops are formed right at the orifice in a dripping process. The inner fluid can form a jet, which breaks into drops further downstream. This paper shows that the transition from dripping to jetting can be characterized by a state diagram that depends on the capillary number of the outer fluid and the Weber number of the inner fluid.

Results

In figure 1, the shear forces of the outer fluid are drive force for forming drops. Dripping occurs as the balance of surface tension and viscous shear force from the outer fluid dictates the size of the break-off drop. Decreasing qin/qout, a jet is formed and the break off point departs from the nozzle of the inner fluid.
Figure 2. Experimentally measured diameter of the jets and resulting drops scaled by D.
Figure 3. Measured drop diameter.

Figure 2 compares with the experimental results. When dripping occurs, the diameter of drops can be measured by a force between shear stress of the outer fluid and the surface tension of the inner fluid. When jetting occurs, the diameter of drops can be determined by the volume in one wavelength of the Rayleigh-Plateau instability which is same as the volume of the drop. Figure 3 illustrates the treads in drop size as a function of qin and uout. Inertia of the inner fluid drives the Rayleigh-Plateau instability and the formed drop. Experimental results show that drop formation includes three steps as following: advection and necking at the end of the jet, pinchoff, and retraction. It takes a long time in the first step, so the dominating time scale will be determined by this part.

Discussion

This research identifies the different jetting responses and highlight the importance of the coflowing viscous liquid in the dripping-to-jetting transition. The two jetting regimes result from a different balance of dominant forces and these two regimes depends on the ability of forces to deform the emerging liquid from a spherical drop to a cylindrical jet. This paper shows two different behaviors occured in co-flowing liquid-liquid microfluidic devices.