Equilibrium shapes and floatability of static and vertically vibrated heavy liquid drops on the surface of a lighter fluid

In a drop of liquid which hangs below a horizontal support or a t the end of a tube, the forces due to surface tension, pressure and gravity are in equilibrium. Amongst the many possible equilibrium shapes of the drop, only those which are stable occur naturally. The calculus of variations has been used to determine theoretically the stable equilibria, by calculating the energy change when the liquid in equilibrium experiences axially symmetrical perturbations under physically realistic constraints. If the energy change can be made negative, the drop is unstable. With this criterion, stable equilibria have been identified through which the naturally growing drops evolve until they reach a maximum volume, when they become unstable. These results are illustrated by calculations relating to typical experimental conditions.

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Equilibrium shapes of acoustically levitated liquid drops

The Journal of the Acoustical Society of America ◽

10.1121/1.2022222 ◽

1985 ◽

Vol 77 (S1) ◽

pp. S20-S21 ◽

Cited By ~ 1

Author(s):

E. Trinh ◽

C. J. Hsu

Keyword(s):

Liquid Drops ◽

Equilibrium Shapes

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Equilibrium shapes of charged droplets and related problems: (mostly) a review

Geometric Flows ◽

10.1515/geofl-2017-0004 ◽

2017 ◽

Vol 2 (1) ◽

Author(s):

Michael Goldman ◽

Berardo Ruffini

Keyword(s):

Electric Field ◽

External Electric Field ◽

Variational Model ◽

Optimal Distribution ◽

Liquid Drops ◽

Charged Droplets ◽

Original Contribution ◽

Ill Posed ◽

Equilibrium Shapes

AbstractWe review some recent results on the equilibrium shapes of charged liquid drops. We show that the natural variational model is ill-posed and how this can be overcome by either restricting the class of competitors or by adding penalizations in the functional. The original contribution of this note is twofold. First, we prove existence of an optimal distribution of charge for a conducting drop subject to an external electric field. Second, we prove that there exists no optimal conducting drop in this setting.

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The shape and stability of rotating liquid drops

Proceedings of the Royal Society of London Series A - Mathematical and Physical Sciences ◽

10.1098/rspa.1980.0084 ◽

1980 ◽

Vol 371 (1746) ◽

pp. 331-357 ◽

Cited By ~ 125

Keyword(s):

Surface Tension ◽

Angular Momentum ◽

Energy Surface ◽

Basis Functions ◽

Liquid Drops ◽

Rotation Rates ◽

Computer Aided Analysis ◽

Rotating Liquid ◽

Computer Aided ◽

Equilibrium Shapes

Equilibrium shapes and stability of rotating drops held together by surface tension are found by computer-aided analysis that uses expansions in finiteelement basis functions. Shapes are calculated as extrema of appropriate energies. Stability and relative stability are determined from curvatures of the energy surface in the neighbourhood of the extremum. Families of axisymmetric, two-, three- and four-lobed drop shapes are traced systematically. Bifurcation and turning points are located and the principle of exchange of stabilities is tested. The axisymmetric shapes are stable at low rotation rates but lose stability at the bifurcation to twolobed shapes. Two-lobed drops isolated with constant angular momentum are stable. The results bear on experiments designed to further those of Plateau (1863).

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