Floating Bubble Configurations

Abstract

The configurations of bubbles floating at a vapor-liquid interface are investigated both analytically and experimentally. The differential equations governing the shape of a single bubble at rest in a liquid of infinite extent are deduced under the assumption of zero dome thickness, uniform surface tension, and equal gas densities within the bubble and above the interface. These equations show that nondimensional bubble shapes depend upon the value of a single parameter. An analytical solution, valid for small bubbles, is developed and shown to be in good agreement with the general numerical solution. Good agreement with theory is demonstrated for floating air bubbles, both stationary and translating, ranging in volume from 0.01 cc (in water) to 0.83 cc (in heavy mineral oil). Theoretical results over a dimensionless bubble volume (the ratio of volume to the cube of the capillary constant) range of from 2.6 × 10−4 to 5527 are given.