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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.

SUBMITTER: Alimov MM

PROVIDER: S-EPMC4075789 | biostudies-literature | 2014 Aug

REPOSITORIES: biostudies-literature

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Meniscus on a shaped fibre: singularities and hodograph formulation.

Alimov Mars M MM Kornev Konstantin G KG

Proceedings. Mathematical, physical, and engineering sciences 20140801 2168

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 w ...[more]

PMID: 25104910

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