We use cookies to ensure that we give you the best experience on our website. You can change your cookie settings at any time. Otherwise, we'll assume you're OK to continue.

Department of Mathematical Sciences

# Seminar Archives

## Numerical Analysis Seminars: A numerical model of the dry spinning process

Presented by Joyce Aitchison (Cranfield),

1 March 2002 14:00 in CM105

"

The dry spinning process is a standard method for the industrial production of synthetic fibres. A polymer is dissolved in a volatile solvent and the solution is pumped through a spinneret with many holes. After the filaments leave the spinneret, the liquid polymer is solidified by evaporating the solvent in a stream of hot air or inert gas. The fibres are then collected on a take-up wheel with a specified speed which also causes them to stretch.

This continuous production process can be modelled as a steady state flow. Specifically in this talk we describe a mathematical model and associated numerical algorithm for the calculation of the behaviour of an axisymmetric polymer filament subject to evaporation and extension. The diffusion of the solvent and the conduction of heat are modelled as nonlinear PDEs. Evaporation of the solvent takes place at the surface of the filament which is an unknown free surface, and must be determined as part of the solution.

The mechanics of the process are modelled by a system of ODEs and algebraic equations which are linked to the diffusion equations above. Boundary values are given for the axial velocity at both the inlet and the outlet, but there are no boundary conditions for the tension. The resulting system of linked algebraic equations, ODEs and PDEs form a boundary value problem in the direction of the spin-line, with an unbalanced set of boundary conditions. Such a system occurs frequently when a continuous manufacturing process is represented by a steady state model.

In this talk we consider the modelling of such a system and the computational issues involved in locating the unknown free surface and the matching of inlet and outlet conditions.

"