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Publication Detail
Instabilities and constitutive modelling
Abstract
The plastics industry today sees huge wastage through product defects caused by unstable flows during the manufacturing process. In addition, many production lines are throughput-limited by a flow speed threshold above which the process becomes unstable. It is therefore critically important to understand the mechanisms behind these instabilities. In order to investigate the flow of a molten plastic, the first step is a model of the liquid itself, a relation between its current stress and its flow history called a constitutive relation. These are derived in many ways, and tested on several benchmark flows, but rarely is the stability of the model used as a criterion for selection. The relationship between the constitutive model and the stability properties of even simple flows is not yet well understood: we show that in one case a small change to the model, which does not affect the steady flow behaviour, entirely removes a known instability; in another, a change which makes a qualitative difference to the steady flow makes only tiny changes to the stability. The long-term vision of this research is to quantify exactly what are the important properties of a constitutive relation as far as stability is concerned. If we could understand that, then not only could very simple stability experiments be used to choose the best constitutive models for a particular material, but our ability to predict and avoid wasteful industrial instabilities would be vastly improved.
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Dept of Mathematics
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