Capillary phenomena. II. Equilibrium and stability of rotationally symmetric fluid bodies

Abstract

A comprehensive method is given for describing in reduced terms pendent drops, emergent bubbles, sessile drops and captive bubbles of a fluid α within a fluid β as figures produced by revolution of their meridian curves ( X , Z ). Boundary conditions at a solid surface are: ( a ) with a constant contact radius X Ɵ ; or ( b ) with a constant contact angle θ . A new curve of maximum pendent-drop or emergent-bubble volume is given for case ( b ); that for case ( a ) was described in part I (Boucher & Evans 1975). The stability of the various capillary system and boundary condition combinations is discussed in detail. In particular, pressure maxima for boundary condition ( a ) are analysed and their applicability to actual systems, involving pistons or syphons to deliver fluid α, is explained. A thermodynamic analysis has been carried out and shown to be appropriate for identifying features pertaining to pressure maxima and volume maxima. The relevance of the study to systems with contact-angle hysteresis, and to more complex geometrical shapes of interface is discussed.