Capillary phenomena. Part 17.—Properties of fluid rings between a sphere above a horizontal plane in a gravitational field

Abstract

The prediction of liquid ring properties for the sphere/plane system has been approached by obtaining accurate fluid/fluid meridian curves and associated quantities, e.g. capillary pressure differences, fluid ring heights and volumes, and by using approximate expressions for limiting configurations. Reduced quantities, which can be related to terrestrial gravity conditions, are compared with some zero-gravity properties.

Provided the horizontal solid is of large extent, fluid rings in a gravitational field (but not at zero g), will reach a maximum height, unless they can completely engulf the sphere. It is not possible for the sphere to be completely enveloped if its radius is r≳ 0.54[2γ(1–cosθ)/Δρg]^½. For contact angles θ > 0°, the ring height tends to a limit as its volume increases, having passed through the height maximum.