## Abstract

We study the capillary rise of viscous liquids into sharp corners formed by two surfaces whose geometry is described by power laws h_{i}(x) = c_{i}x^{n}, i = 1, 2, where c_{2} > c_{1} for n ≥ 1. Prior investigations of capillary rise in sharp corners have shown that the meniscus altitude increases with time as t^{1/3}, 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 c_{i} and n, which gives rise to the universal t^{1/3} 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 c_{i} 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 language | English (US) |
---|---|

Article number | A26 |

Journal | Journal of Fluid Mechanics |

Volume | 978 |

DOIs | |

State | Published - Jan 5 2024 |

## All Science Journal Classification (ASJC) codes

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

## Keywords

- capillary flows
- lubrication theory