Abstract

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, κ-1, and the container radius, L, is varied from a small value comparable to R to ∞. In the limit of L≪κ-1, we analytically solve the general Young-Laplace equation governing the meniscus profile and show that the meniscus height, Δh, scales approximately with Rln(L/R). In the opposite limit where L≫κ-1,Δh becomes independent of L and scales with Rln(κ-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 0.4κ-1≲L≲4κ-1. An approximate analytical expression has been found for Δh, enabling its accurate prediction at any values of L that ranges from microscopic to macroscopic scales.

Talk to us

Join us for a 30 min session where you can share your feedback and ask us any queries you have

Schedule a call

Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.