Boundary integral method for the evolution of slender viscous fibres containing holes in the cross-section

Abstract

We consider the evolution of slender viscous fibres with cross-section containing holes with application to fabrication of microstructured optical fibres. The fibre evolution is driven by either prescribing velocity or a force at the ends of the fibre, and the free surfaces evolve under the influence of surface tension, internal pressurization, inertia and gravity. We use the fact that ratio of the typical fibre radius to the typical fibre length is small to perform an asymptotic analysis of the full three-dimensional Navier–Stokes equations similar to earlier work on non-axisymmetric (but simply connected) fibres. A numerical solution to the multiply connected steady-state drawing problem is formulated based on the solution the Sherman–Lauricella equation. The effects of different drawing and material parameters like surface tension, gravity, inertia and internal pressurization on the drawing are examined, and extension of the method to non-isothermal evolution is presented.