The meniscus on the outside of a circular cylinder: From microscopic to macroscopic scales

We systematically study the meniscus on the outside of a small circular cylinder vertically immersed in a liquid bath in a cylindrical container that is coaxial with the cylinder. The cylinder has a radius R much smaller than the capillary length, kappa(-1), and the container radius, L, is varied from a small value comparable to R to CO. In the limit of L << kappa(-1) we analytically solve the general Young-Laplace equation governing the meniscus profile and show that the meniscus height, Delta h, scales approximately with RIn(L/R). In the opposite limit where L >> kappa(-1), Delta h becomes independent of L and scales with R ln(kappa(-1)/R). We implement a numerical scheme to solve the general Young-Laplace equation for an arbitrary L and demonstrate the crossover of the meniscus profile between these two limits. The crossover region has been determined to be roughly 0.4 kappa(-1) less than or similar to L less than or similar to 4 kappa(-1). An approximate analytical expression has been found for Ah, enabling its accurate prediction at any values of L that ranges from microscopic to macroscopic scales. (C) 2018 Elsevier Inc. All rights reserved.