Abstracts - KTH Mechanics

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Continuum Models in Industrial Applications.
Hilary Ockendon a
A continuum model is often a model at the macrolevel of a process which has a
very complicated discrete structure at the microlevel. This talk describes some
situations in which a relatively simple continuum model can be used to give
useful results in an industrial setting. Two cases will be considered.
1. The Fanno model is traditionally used to model turbulent gas flow in
long pipes. The unsteady version of this model turns out to be
appropriate for problems as diverse as explosions in coalmines, pressure
transducers in extreme situations and the high speed spinning of
manmade fibres. These applications show that a well-known model can
still contain unexpected results.
2. A more unconventional modelling task is posed by the deformation of a
mass of entangled fibres. Here the dynamics of the microstructure are
governed by frictional interactions between fibres and the bending and
stretching of individual fibres. In spite of the complicated
microstructure, it is possible to construct a useful macroscopic model of
the material as an anisotropic viscous fluid when it is in tension and as a
linear anisotropic elastic material when in compression. The model
builds on ideas from liquid crystals and fibre reinforced materials and
introduces the concept of “entanglement” to quantify the state of the
material. Practical examples include the movement of fibres in the
carding machine and the packing of glass fibre insulation.
a Mathematical Institute, University of Oxford, 24-29 St Giles, Oxford