Equilibrium Shape of Ferrofluid in the Uniform External Field

Report No. ARL-TR-8058
Authors: Michael Grinfeld; Pavel Grinfeld
Date/Pages: July 2017; 16 pages
Abstract: It is well known that the morphology of magnetic or electric ferrofluids is extremely sensitive to the applied external electromagnetic fields. Even in the static regimes, they demonstrate a variety of qualitative and quantitative transformations often mentioned as free-surface instabilities. That makes their computational modeling rather challenging. For the sake of validation and verification, there is a need for having exact solutions. Modelers noticed that quite often isolated ferrofluids take on the shape of a spheroid co-axial with the applied quasi-uniform field. There were several claims that a consistent theory allows researchers to prove that an isolated drop of ferrofluid exposed to a uniform field, indeed, has a shape of a spheroid. This report will analyze the computational algorithm that allows us to resolve this and similar problems numerically.
Distribution: Approved for public release
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Last Update / Reviewed: July 1, 2017