The shape of a pendent liquid drop
Abstract
Formal solutions of the static equilibrium equations for the form of the outer surface of a pendent liquid drop are studied. An approach is adopted in which only the oneparameter family determined by vertex height (u sub 0) need be described. Attention is restricted to rotationally symmetric configurations, and all symmetric solutions are characterized for the case where the Lagrange parameter lambda is equal to zero. It is shown that for any u sub 0 the function u(r; u sub 0) can be extended as a parametric solution of a system of equations for all arc lengths, yielding a curve without limit sets or double points, and that the resulting capillary rotation surface spreads out indefinitely away from the axis r = 0. The asymptotic form of the surface in the case of large absolute values of u sub 0 is characterized quantitatively, along with the global structure of all such surfaces.
 Publication:

Philosophical Transactions of the Royal Society of London Series A
 Pub Date:
 August 1979
 DOI:
 10.1098/rsta.1979.0064
 Bibcode:
 1979RSPTA.292..307C
 Keywords:

 Applications Of Mathematics;
 Drops (Liquids);
 Fluid Mechanics;
 Space Commercialization;
 Asymptotic Methods;
 Geometry;
 Integral Equations;
 Singularity (Mathematics);
 Fluid Mechanics and Heat Transfer