Toroidal instabilities in the presence of charge and non-Newtonian fluids

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Fragkopoulos, Alexandros A.
Fernandez-Nieves, Alberto
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Cylindrical jets break into spherical droplets due to surface-tension driven, Rayleigh-Plateau instabilities. Interestingly, toroidal droplets can also transform into a spherical droplet via a shrinking instability whereby the handle of the torus progressively disappears. We study this instability using particle image velocimetry and determining the velocity field inside the droplet. Using the experiments as a guide, we theoretically analyze the problem and account for the discrepancy between previous theoretical and simulation work. This allows elucidating which of the many possible modes controlling the toroidal droplet evolution are needed to capture the evolution and deformation of the droplet as seen experimentally. We then apply a voltage difference across the droplet and a controlled ground to charge the toroidal droplet. In this case, surface tension stresses compete with electrostatic stresses due to the presence of surface charge; qualitatively changing the behavior of the droplet, which, for sufficiently high voltages, is able to transition from a shrinking torus to an expanding torus. Remarkably, an additional transition happens at even higher voltages; in this case, the torus produces finger-like structures reminiscent of the Saffman-Taylor instability. Despite the three-dimensional character of our experiments, charge and geometry both combine to allow observing an instability that is most often seen in quasi-two dimensional situations. We study and model all these transitions, and identify the essential physics needed to describe them. Finally, we exploit that thin toroidal droplets approach the cylindrical limit to also study the effect of charge over jet break-up. We do this by comparing the experimentally determined wavelength associated to the fastest unstable mode to theoretical expectation for charged cylindrical jets. Furthermore, we study the break-up dynamics in the presence of rheologically non-linear materials. In this case, the droplets resist break-up for long times compare to when we use simple liquids. We show that we can explain our data by incorporating the non-linearities into a linear treatment of the problem through the strain-rate-dependent viscosity.
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