Mathematical modelling of a viscida network

Author: 

Griffiths, I
Mavroyiakoumou, C
Howell, P

Publication Date: 

7 June 2019

Journal: 

Journal of Fluid Mechanics

Last Updated: 

2021-08-29T21:30:52.51+01:00

Volume: 

872

DOI: 

10.1017/jfm.2019.364

page: 

147-176

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 partial differential equations and algebraic conservation laws, for a system of viscidas connected at 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 and or 3. We also demonstrate that there is no uniquely defined junction model to describe interconnections between viscidas of different thicknesses.

Symplectic id: 

994726

Submitted to ORA: 

Submitted

Publication Type: 

Journal Article