Non-coalescence of oppositely charged drops

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Original entry: Sujit S. Datta, APPHY 225, Fall 2009.

Reference

W. D. Ristenpart, J. C. Bird, A. Belmonte, F. Dollar and H. A. Stone, Nature 461, 377 (2009).

Keywords

electric, droplet, coalescence, dielectrophoresis

Key Points

The objective of this work was to study the coalescence behavior of water droplets (dispersed in oil) under the influence of an applied electric field. The experimental setup was simple: the bottom half of a container was filled with water and was electrically grounded, while the top half was filled with a poorly conducting oil, with an electrode inserted in the liquid. This allows an inhomogeneous electric field (of strength up to 100,000V/m) to be applied across the sample chamber. After this field is applied, a small water droplet is pipetted into the oil at the top of the chamber. Because the electric field is inhomogeneous, the droplet moves by dielectrophoresis towards the top electrode. Upon contact, the droplet picks up a charge (say positive) and is subsequently repelled from the top electrode and attracted toward the water in contact with the bottom electrode. What happens at this point?

The central result of this work is the following surprising result: for sufficiently small electric force and salt concentration of the water droplet, the droplet contacts and coalesces with the water filling the bottom half of the sample chamber (this itself is unsurprising, because the droplet is attracted to the `grounded' water), while for an electric force larger than a critical value (that is a function of the salt concentration), the droplet bounces off the lower oil-water interface. This is surprising: while the droplet is electrically attracted to the oppositely-charged lower large water droplet, upon contact, it does not coalesce but is, in fact, repelled. This effect can be generalized: for example, the authors of this paper show a nice example of how individual droplets in a "train" of droplets can "shuttle" charge back and forth between each other via this non-coalescence bouncing process.

What is the explanation for this counter-intuitive behavior? For starters, it is important to note that electrostatics dominates in this system, and inertia does not play a role: the Reynolds number is ~0.01. When a charged droplet comes close to contacting another (oppositely) charged droplet, the electrical stress acting on the liquid/liquid interface deforms it into a conical shape, often referred to as a "Taylor cone". When the droplet approaches sufficiently close to the other droplet, a small, short-lived liquid bridge is formed between the two, and charge is transferred from one to the other, probably by ionic conduction through the water. The droplets are now equally charged, and the dynamics of the system are governed by a competition between the capillary pressure associated with the liquid bridge (which favors coalescence) and electrostatic repulsion (which favors non-coalescence and droplet "bouncing"). Because the capillary pressure depends on the geometry of the Taylor cone (in particular, how "pointy" it is), which in turn depends on the applied field strength and droplet charge. For sufficiently large field strength or droplet charge - that is, for sufficiently large electric force - the Taylor cone is so elongated that the electrostatic repulsion between the two droplets wins out over the capillary pressure associated with the liquid bridge between the two droplets.