Capillary phenomena. Part 24.—Properties of fluid bridges between solid rods in a gravitational field

Abstract

Properties are predicted in dimensionless terms for fluid bridges between vertically aligned rods in a gravitational field. Meridian curves, which on rotation give the bridges, have been obtained for reduced rod radii R= 0.5–10.0. Actual rod radii are given by r=aR, where the capillary constant a is ca. 3.8 mm for water bridges in air and 8 mm for silicon at its freezing point in an inert atmosphere subjected to terrestrial gravity. Properties such as the pressure difference across the bridge interface and the force on the upper rod have been obtained for cases of varying fluid volume at several fixed rod-separation distances and of varying rod separation at fixed volumes. Stability limits as well as equilibrium paths are discussed. The results also provide a basis for analysing ideal float-zone refining, e.g. a silicon zone formed from its own solid: in these cases there are limitations on the fluid volume and on the angle of inclination of the fluid interface needed for solidification of a rod of purified material of uniform radius. Taking a growth angle of 11° for silicon, the maximum rod radius that can be grown from a zone of melt is ca. 40 mm.