Capillary phenomena. Part 18.—Conditions for the flotation of solid spheres at liquid/liquid and liquid/vapour interfaces in a gravitational field

Abstract

Conditions for unaided sphere flotation at fluid/fluid interfaces are explicitly given in reduced terms using density parameters k^α=(ρ^s–ρ^α)/Δρ and k^β=(ρ^s–ρ^β)/Δρ, where Δρ is the positive density difference between fluids α and β. The method given entails the minimum of numerical computation needed to give the limits for stable flotation: at the limits the sphere detaches and either rises or sinks. Representative accurate data illustrate the range of flotation depending on the contact angle and the sphere radius. Two approximations are also discussed.