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Mathematical modelling of a viscida network

  • C. Mavroyiakoumou (a1), I. M. Griffiths (a2) and P. D. Howell (a2)

Abstract

We develop a general model to describe a network of interconnected thin viscous sheets, or viscidas, which evolve under the action of surface tension. A junction between two viscidas is analysed by considering a single viscida containing a smoothed corner, where the centreline angle changes rapidly, and then considering the limit as the smoothing tends to zero. The analysis is generalized to derive a simple model for the behaviour at a junction between an arbitrary number of viscidas, which is then coupled to the governing equation for each viscida. We thus obtain a general theory, consisting of $N$ partial differential equations and $3J$ algebraic conservation laws, for a system of $N$ viscidas connected at $J$ junctions. This approach provides a framework to understand the fabrication of microstructured optical fibres containing closely spaced holes separated by interconnected thin viscous struts. We show sample solutions for simple networks with $J=2$ and $N=2$ or 3. We also demonstrate that there is no uniquely defined junction model to describe interconnections between viscidas of different thicknesses.

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Corresponding author

Email address for correspondence: ian.griffiths@maths.ox.ac.uk

References

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