Capillary phenomena. Part 8.—Bridge meridians for fluid interfaces with solids in cylindrical vessels: computation, bessel approximations and comparison of properties of finite and infinite systems

Abstract

Capillary phenomena previously predicted for rods in fluids of large interfacial extent, given by holms which asymptotically approach zero interfacial curvature at infinite radius, are compared with rods of radius R₂ in vessels of radius R₁. The difference between the systems is attributed to: (i) a vessel-wall effect depending on the contact angle at the wall, or, on a solid edge three-phase confluence condition; and (ii) the finite and fixed volume of one of the fluids implied by the finite vessel. Procedures for obtaining meridian curves for shallow broad bridges in terms of Bessel functions are given. Numerical computation is necessary for meridians inclined at ≳ 10° to the horizontal.

It is not thought practicable, as a general procedure, to compute theoretical meridians and attendant quantities, for comparison with experiment, for systems bounded by two solids because of their complexity. However, it is concluded that, in general, experimental conditions can be used such that the difference in behaviour between finite and infinite systems can be made insignificant. For example, the capillary rise up a rod of reduced radius R₂= 0.5 dipped in a liquid, and the excess force on this rod, differ insignificantly from the infinite case when the vessel radius exceeds R₁= 20. For water/air interfaces the actual radii would be about 2 mm and 80 mm respectively. Other examples are examined in detail.