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Isaac Newton Institute for Mathematical Sciences

Evolution and formation of singularities on electrically charged fluid masses: modelization, analysis and numerical simulation.

Presenter: Lucia Belen Gamboa Salazar (Predoctoral student in ICMAT)

Co-author: Marco Antonio Fontelos Lopez ( ICMAT Research Scientist)

Abstract

When a conductive fluid is electrically charged, the dynamic behavior can be very different from the behavior in the absence of charge. The electrical charges tend to migrate to the surface and, once there, they suffer electrostatic repulsion forces. These forces are trying to destabilize all the fluid, which in absence of that forces would tend to adopt stable configurations. The instability results, in many cases, the emission of fluid microjets at certain points of the surface. This issue of microjets is the fundamental mechanism of electrospray techniques that allow the generation of microscopic droplets. It is also the foundation of the so-called colloidal thrusters used in micropropulsion. A classical result by Rayleigh establishes a viscous drop of a perfectly conducting liquid should become unstable for a large enough value of the net electric charge contained by the drop. We compute the correction to this result due to the fact that the drop, instead of containing a perfectly conducting fluid, contains a dielectric liquid with ions (electrolytes) dissolved. One particular issue that can be analyzed is the formation of the so-called Rayleigh jets that appear when a drop contains a supercritical amount of electric charges. It has been previously shown that when the fluid is perfectly conducting Rayleigh jets do not appear but instead conical tip singularities at the interface develop in finite time (cf. [1], [2]). We show that Rayleigh jets appear due to the corrections introduced by considering a finite ion mobility or equivalently, by replacing the Maxwell stress tensor for a perfect conductor by an asymptotic expressions that we obtained. [1] S. I. Betelu, M. A. Fontelos, U. Kindelan and O. Vantzos, Sigularities on charged drops, Phys. Fluids 18, 051706 (2006). [2] M. A. Fontelos, U. Kindelan and O. Vantzos, Evolution of neutral and charged droplets in an electric field, Phys. Fluids 20 (2008), 092110.