Capillary phenomena - III. Properties of rotationally symmetric fluid bodies with one asymptote - holms

Abstract

Rotationally symmetric fluid bodies having an asymptote $X$ $\rightarrow $ $\infty $ with the horizontal plane and meeting a solid at $Z$ = $Z$$^{\oplus}$, and whose meridian is $Z=Z(X)$, are called holms. Holms meeting a vertically-positioned solid cylindrical rod at its lower edge where $X$ = $X$$^{\oplus}$, or a solid sphere of radius $R$ where the angle of contact is $\theta $, lead to capillary phenomena which are described following the approach of parts I and II (Boucher & Evans 1975; Boucher, Evans & Kent 1976). Detachment of a rod will occur at a maximum in the force applied to it (i.e. the excess force due to the presence of the holm), or at a maximum in $Z$$^{\oplus}$, depending on the mechanical system. For the former, the mechanical device needs to be undamped, whereas for the latter, a rigid arrangement is required. The characteristic quantities for these two cases, which are analogous to the volume maxima and pressure maxima of pendent drops (parts I and II), are tabulated. The behaviour expected of a sphere which is floating, or of one which is subjected to a vertically applied force, is also considered. Spontaneous changes which can occur when an equilibrium meridian gives an unstable configuration, as with a hole formed in a sheet of liquid on a solid surface, are discussed where contact-angle hysteresis exists. The account given in part I on detachment methods of interfacial tension determination is extended. The appendix shows the range of accuracy of Bessel function approximations to the meridia of holms, pendent and sessile drops, and emergent and captive bubbles.