Stokes flow singularities in a two-dimensional channel: a novel transform approach with application to microswimming | Zendy

Darren Crowdy | Zendy; Anthony M. J. Davis | Zendy

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Stokes flow singularities in a two-dimensional channel: a novel transform approach with application to microswimming

Author(s) -

Darren Crowdy,

Anthony M. J. Davis

Publication year - 2013

Publication title -

proceedings of the royal society a mathematical physical and engineering sciences

Language(s) - English

Resource type - Journals

eISSN - 1471-2946

pISSN - 1364-5021

DOI - 10.1098/rspa.2013.0198

Subject(s) - biharmonic equation , polygon (computer graphics) , stokes flow , channel (broadcasting) , fourier transform , gravitational singularity , flow (mathematics) , mathematics , mathematical analysis , geometry , boundary value problem , computer science , telecommunications , frame (networking)

A transform method for determining the flow generated by the singularities of Stokes flow in a two-dimensional channel is presented. The analysis is based on a general approach to biharmonic boundary value problems in a simply connected polygon formulated by Crowdy & Fokas in this journal. The method differs from a traditional Fourier transform approach in entailing a simultaneous spectral analysis in the independent variables both along and across the channel. As an example application, we find the evolution equations for a circular treadmilling microswimmer in the channel correct to third order in the swimmer radius. Significantly, the new transform method is extendible to the analysis of Stokes flows in more complicated polygonal microchannel geometries.

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