External meniscus on a thin fiber with flattened sides

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.