Capillary phenomena. IV. Thermodynamics of rotationally-symmetric fluid bodies in a gravitational field

Abstract

A thermodynamic treatment is given of rotationally-symmetric fluid bodies in a gravitational field, termed pendent and sessile drops, captive and emergent bubbles, and holms, meeting solid bodies at constant contact radius Xe , or constant contact angle θ. Parts I, II and III (Boucher & Evans 1975; Boucher, Evans & Kent 1976; Boucher & Kent 1977 a), give the properties of these systems, mainly on the basis of the numerical computations of their meridia. The analyses yield expressions for the equilibrium of a system following a path, e.g. with the enveloped-bubble volume Va> e as the independent variable. Of importance for the experimental use of these systems, in e.g. interfacial tension determination, are the conditions for the onset of instabilities depending on the conditions: e.g. captive bubbles and sessile drops have pressure maxima with Xe constant, but not for θ constant. With holms meeting solid bodies, e.g. rods and spheres, the height of the solid is an independent variable, and especially with spheres, the predicted behaviour relating to their detachment is complex. The study reveals the distinction between absolute and excess (differential) applied-force on mechanically raising solids. The detection of instabilities depends on a distinction between stress-controlled and strain-controlled mechanical manipulation of an experimental system. The general presentation permits extensions of the treatment to other physically realizable systems. Features of the holm systems occur with technologically important processes (e.g. crystal growth from the melt).