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Electrically Charged Toroidal Droplets

Alexandros A. Fragkopoulos, Ekapop Pairam, and Alberto Fernandez-Nieves

Introduction

Toroidal droplets are unstable due to surface tension and they destabilize in two different ways depending on the aspect ratio (defined on figure below.) For ξ<2 the torus shrinks until it collapses into a sphere, while for ξ>2 the torus breaks up into spherical droplets.


Fig. 1: Left: Shrinking instability. Middle: Rayleigh-Plateau instability. Right: define geometric parameters.

The goal of this project is to see how the effect of charge changes the evolution of a toroidal droplet. We observe that a charged torus transitions from a shrinking torus to an expanding torus with increasing charge, and that the break up droplets increase in number with increasing charge.

Experimental Setup

Figure 2 shows the experimental setup that we use to perfomr the experiments. On top of the rotating stage we have a cuvet tha includes our outer liquid, 30,000 cSt silicone oil. Using a metallic needle we pump the inner liquid, glycerol, and a toroidal dropelt is formed. We then apply a voltage difference across the torus and the rotating stage, and we measure the current using a picoammeter. Finally, we observe the evolution from below using a CCD camera.

Fig. 2: Schematic of the experimental setup.

Demonstration of a torus forming.

Major Observations

There are two major observation as we increase the voltage applied. The first one is that the torus does not shrink anymore, but rather expands as we increase the voltage. The other is that the number of droplets that we observe as the torus breaks increases with applied voltage. Both of these phenomena are observed on the following videos. The videos show the evolution of tori with almost the same aspect ratio, ξ≈4.9, but at different voltages

V = 1500 Volts

V = 3000 Volts

Left, torus with ξ≈4.9 and V=1500Volts. Right, torus with ξ≈4.9 and V=3000Volts. Both tori start almost with the same aspect ratio, but the low voltage shrinks and breaks into two droplets, while the high voltage expands and breaks into three droplets.
References:
[1] Pairam E, Fernandez-Nieves A, Generation and stability of toroidal droplets in a viscous liquid, Phys. Rev. Lett. 102, 234501 (2009).

[2] Wang Q, Papageorgiou DT, Dynamics of a viscous thread surrounded by another viscous fluid in a cylindrical tube under the action of a radial electric field: breakup and touchdown singularities, J. Fluid Mech. 683, 22-56 (2011).

Soft Condensed Matter Laboratory, School of Physics, Georgia Institute of Technology
770 State Street NW, Atlanta, GA, 30332-0430, USA
Phone: 404-385-3667 Fax: 404-894-9958
alberto.fernandez [at] physics.gatech.edu