# Determining surface tension using DC magnetic levitation

Easter, S., Bojarevics, Valdis and Pericleous, Koulis A. (2009) *Determining surface tension using DC magnetic levitation.* 6th International Conference on Electromagnetic Processing of Materials, EPM 2009. Forschungszentrum Dresden-Rossendorf, Dresden, Germany. ISBN 978-3-936104-65-3

## Abstract

The values of material physical properties are vital for the successful use of numerical simulations for electromagnetic processing of materials. The surface tension of materials can be determined from the experimental measurement of the surface oscillation frequency of liquid droplets. In order for this technique to be used, a positioning field is required that results in a modification to the oscillation frequency. A number of previous analytical models have been developed that mainly focus on electrically conducting droplets positioned using an A.C. electromagnetic field, but due to the turbulent flow resulting from the high electromagnetic fields required to balance gravity, reliable measurements have largely been limited to microgravity. In this work axisymmetric analytical and numerical models are developed, which allow the surface tension of a diamagnetic droplet positioned in a high DC magnetic field to be determined from the surface oscillations. In the case of D.C. levitation there is no internal electric currents with resulting Joule heating, Marangoni flow and other effects that introduce additional physics that complicates the measurement process. The analytical solution uses the linearised Navier-Stokes equations in the inviscid case. The body force from a DC field is potential, in contrast to the AC case, and it can be derived from Maxwell equations giving a solution for the magnetic field in the form of a series expansion of Legendre polynomials. The first few terms in this expansion represent a constant and gradient magnetic field valid close to the origin, which can be used to position the droplet. Initially the mathematical model is verified in microgravity conditions using a numerical model developed to solve the transient electromagnetics, fluid flow and thermodynamic equations. In the numerical model (as in experiment) the magnetic field is obtained using electrical current carrying coils, which provides the confinement force for a liquid droplet. The model incorporates free surface deformation to accurately model the oscillations that result from the interaction between the droplet and the non-uniform external magnetic field. A comparison is made between the analytical perturbation theory and the numerical pseudo spectral approximation solutions for small amplitude oscillations.

Item Type: | Book Section |
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Additional Information: | This was a poster session and forms part of the Proceedings of the 6th International Conference on Electromagnetic Processing of Materials, EPM2009, held 19-23 October 2009, in Dresden, Germany. EPM2009 was jointly coordinated by the Institute of Safety Research of the Forschungszentrum Dresden-Rossendorf (FZD), Germany and SIMaP/EPM Grenoble, France. |

Uncontrolled Keywords: | magnetic levitation, material physical properties, surface tension, analytical models |

Subjects: | T Technology > TS Manufactures Q Science > QA Mathematics |

School / Department / Research Groups: | School of Computing & Mathematical Sciences > Centre for Numerical Modelling & Process Analysis School of Computing & Mathematical Sciences School of Computing & Mathematical Sciences > Department of Computer Systems Technology School of Computing & Mathematical Sciences > Department of Mathematical Sciences School of Computing & Mathematical Sciences > Centre for Numerical Modelling & Process Analysis > Computational Science & Engineering Group |

Related URLs: | |

Last Modified: | 31 Mar 2011 18:20 |

URI: | http://gala.gre.ac.uk/id/eprint/1495 |

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