Capillary rise in sharp corners: not quite universal

Katie Wu, C. Duprat, H. A. Stone

Research output: Contribution to journalArticlepeer-review

Abstract

We study the capillary rise of viscous liquids into sharp corners formed by two surfaces whose geometry is described by power laws hi(x) = cixn, i = 1, 2, where c2 > c1 for n ≥ 1. Prior investigations of capillary rise in sharp corners have shown that the meniscus altitude increases with time as t1/3, a result that is universal, i.e. applies to all corner geometries. The universality of the phenomenon of capillary rise in sharp corners is revisited in this work through the analysis of a partial differential equation for the evolution of a liquid column rising into power-law-shaped corners, which is derived using lubrication theory. Despite the lack of geometric similarity of the liquid column cross-section for n > 1, there exist a scaling and a similarity transformation that are independent of ci and n, which gives rise to the universal t1/3 power law for capillary rise. However, the prefactor, which corresponds to the tip altitude of the self-similar solution, is a function of n, and it is shown to be bounded and monotonically decreasing as n → ∞. Accordingly, the profile of the interface radius as a function of altitude is also independent of ci and exhibits slight variations with n. Theoretical results are compared against experimental measurements of the time evolution of the tip altitude and of profiles of the interface radius as a function of altitude.

Original languageEnglish (US)
Article numberA26
JournalJournal of Fluid Mechanics
Volume978
DOIs
StatePublished - Jan 5 2024

All Science Journal Classification (ASJC) codes

  • Condensed Matter Physics
  • Mechanics of Materials
  • Mechanical Engineering
  • Applied Mathematics

Keywords

  • capillary flows
  • lubrication theory

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