title: Meniscus on a shaped fibre: singularities and hodograph formulation.
abstract: Using the method of matched asymptotic expansions, the problem of the capillary rise of a meniscus on the complex-shaped fibres was reduced to a nonlinear problem of determination of a minimal surface. This surface has to satisfy a special boundary condition at infinity. The proposed formulation allows one to interpret the meniscus problem as a problem of flow of a fictitious non-Newtonian fluid through a porous medium. As an example, the shape of a meniscus on a fibre of an oval cross section was analysed employing Chaplygin's hodograph transformation. It was discovered that the contact line may form singularities even if the fibre has a smooth profile: this statement was illustrated with an oval fibre profile having infinite curvature at two endpoints.
authors.affiliation: Lobachevsky Institute of mathematics, Kazan Federal University , Kazan, Russia.
authors.forename: Mars M
authors.initials: MM
authors.lastname: Alimov
authors.affiliation: Department of Materials Science and Engineering , Clemson University , Clemson, SC, 29634-0971, USA.
authors.forename: Konstantin G
authors.initials: KG
authors.lastname: Kornev
keywords: capillary rise; complex variables; hodograph transformation; matched asymptotics; minimal surfaces; singularities
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