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Title: Capillary rise in sharp corners: not quite universal
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 $n \geq 1$. Prior investigations of capillary rise in sharp corners have shown that the meniscus altitude increases with time as $t^{1/3}$, a result which 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 exists 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 $n\to \infty$. 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.  more » « less
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Journal of Fluid Mechanics (Cambridge University Press)
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Journal of Fluid Mechanics
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Medium: X
Sponsoring Org:
National Science Foundation
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