Capillary phenomena. Part 22.—Stability regarding solids displaced at interfaces, pendent-drop formation and drainage models subject to various mechanical conditions

Abstract

The displacement of a solid rod vertically aligned at a fluid/fluid interface by a mechanical linkage involving a tensile spring constant K shows critical stability when the volume of the fluid raised by the rod and the rod height are related by dV^α/dZ^⊖=–K. The ideal strain- and stress-controlled limits of stability correspond to K=∞ and K= 0, but intermediate instability is possible. The growth of a pendent drop beneath a tip of radius R, having an open-ended internal capillary bore R′, gives analogous critical stability limits in terms of the pressure difference ΔP^⊖ across the fluid/fluid interface at the tip: d(ΔP^⊖)/dV^α=–2/π(R′)². The analysis is extended to capillaries of sloping internal bore. A brief thermodynamic analysis in terms of the total Helmholtz free energy change is entirely compatible with the phenomenological study. The same principles will apply to more complicated systems of solid detachment and fluid drainage from a porous solid or compact, provided that in the latter film drainage is ignored and only interface displacement is important.