This article is cited in 2 papers

External meniscus on a thin fiber with flattened sides

M. M. Alimov^a, K. G. Kornev<sup>b

a</sup> Kazan Federal University, 18 Kremlyovskaya str., Kazan, 420008 Russia
^b Clemson University, Clemson, SC, USA

Abstract: The previously developed asymptotic method fails short to describe meniscus on a vertical fiber when the fiber has finite straight pieces of its contour in the fiber cross-sections: the theory erroneously gives an infinite height of meniscus at these spots. Here the method has been generalized to include completely wettable fiber with flattened sides. When there are only separate points with zero curvature of the fiber profile and this profile is smooth and convex, the asymptotic approach quite satisfactorily predicts the shape of the meniscus. But it does not adequately reflect the behavior of the contact line in a small neighborhood of the point with zero curvature of the fiber contour: instead of an expected smooth line, we found a contact line with nonsmooth tangent.

Keywords: capillary rise, minimal surface, matched asymptotics, complex variable.

UDC: 532.62:532.546

Received: 16.01.2019
Revised: 16.01.2019
Accepted: 19.06.2019

DOI: 10.26907/0021-3446-2020-1-3-10

 English version: Russian Mathematics (Izvestiya VUZ. Matematika), 2020, 64:1, 1–7

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