Commun. Comput. Phys., 2 (2007), pp. 640-661.


Simulation of Liquid Metal Droplets from Field Emission

Anton VanderWyst 1*, Andrew Christlieb 2, Mark Sussman 3, Iain D. Boyd 4

1 Raytheon Missile Systems, 1151 E. Hermans Road, P.O. Box 11337, Tucson, AZ 85734, USA.
2 Department of Mathematics, Michigan State University, East Lansing, MI 48824, USA.
3 Department of Mathematics, Florida State University, Tallahassee, FL 32306, USA.
4 Department of Aerospace Engineering, University of Michigan, Ann Arbor, MI 48109, USA.

Received 19 September 2006; Accepted (in revised version) 28 November 2006
Available online 8 January 2007

Abstract

Liquid metal droplets are accelerated by electrostatic forces in a process known as field emission. In this study, we simulate the emission of charged indium droplets on a needle in 2D cylindrical coordinates. The boundary element method is used to rapidly and accurately calculate the electric field on the fluid surface, which is then advected forward in time using level sets. This is the first time these methods have been combined, and this combination addresses difficult detachable surface tracking issues successfully. A histogram of droplet charge-to-mass ratio is generated in which it is predicted that smaller satellite droplets are more densely charged. In addition, our model is compared with independent pre- and post-snap off data and produces good agreement with the result.

AMS subject classifications: 65C20, 65M06, 65N38, 65Z05, 74S15, 76B45, 81T80
PACS: 47.11.-j, 47.11.Hj, 79.70.+q
Key words: Field emission electric propulsion, modeling, level set, boundary element method.

*Corresponding author.
Email: Anton_Vanderwyst@raytheon.com (A. VanderWyst), christlieb@math.msu.edu (A. Christlieb), sussman@math.fsu.edu (M. Sussman), iainboyd@umich.edu (I. D. Boyd)
 

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