Capillary phenomena. Part 6.—Behaviour associated with the flotation and mechanical manipulation of solid spheres at fluid interfaces

Abstract

Solid sphere behaviour at the interface between two immiscible fluids will depend on whether or not it can float unaided, or, on the type of device used to manipulate it by an applied force. A thermodynamic treatment is given which leads to equilibrium conditions and to criteria for the stability of the system. Numerically computed meridian curves for the fluid body (holm) meeting a sphere with contact angle θ, and computed interfacial areas and centres of mass of the phases, enable the thermodynamic expressions to be evaluated: they lead to a graphical interpretation of behaviour. The thermodynamic analysis gives criteria for the equilibrium and stability of spheres manipulated by an absolute applied force, and by a differential apparatus with a reference sphere. In either case, criteria are given for maxima in the applied force (holm volume) detectable with a stress-controlling device. To increase the sphere height, a strain-controlling arrangement is required. There are maxima in the height Z^⊖ of the three-phase confluence, and in the sphere position Z^X(above which meridia cease to exist). It is not certain when such a system would become unstable. The behaviour of solid rods and cones is briefly described for comparison.