Equilibrium shapes of two and three dimensional two-phase rotating fluid drops with surface tension: effects of inner drop displacement
Date
2022-11-01
Authors
Butler, Samuel
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American Institute of Physics
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Abstract
The shapes of rotating fluid drops held together by surface tension is an important field
of study in fluid mechanics. Recently, experiments with micron-scale droplets of liquid
helium have been undertaken and it has proven useful to compare the shapes of the resultant
superfluid droplets with classical analogs. If the helium is a mixture of He3 and He4, two
phases are present. In a recent paper, the shapes of rotating two phase fluid droplets were
calculated where the inner drop was constrained to stay at the drop center. The outer
shapes and dimensionless rotation rate-angular momentum relationships were shown to
be similar to single phase drops provided that the density and surface tension scales were
chosen appropriately. In the current paper, I investigate models in which the inner drop can
displace from the centre. In order to simplify the analyses, two dimensional drops are first
investigated. I show that the inner drop is unstable in the centre position if its density is
greater than the outer density and that the inner drop will move towards the outer boundary
of the drop in these cases. When the inner drop has a higher density than the outer drop,
the moment of inertia of displaced inner drops is increased relative to centered drops and
hence the kinetic energy is decreased. Shapes of two and three dimensional drops, rotation
rate-angular momentum and kinetic and surface energy relationships are investigated for
off-axis inner drops with parameters relevant to recent liquid He experiments.
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Keywords
fluid, drop, surface tension
Citation
S.L. Butler (2022), Equilibrium shapes of two and three dimensional two-phase rotating fluid drops with surface tension: effects of inner drop displacement, Physics of Fluids, vol. 34, DOI: 10.1063/5.0121208
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Citation
S.L. Butler (2022), Equilibrium shapes of two and three dimensional two-phase rotating fluid drops with surface tension: effects of inner drop displacement, Physics of Fluids, vol. 34, DOI: 10.1063/5.0121208
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DOI
DOI: 10.1063/5.0121208