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 one-parameter 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.